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TextBox border radius style in WPF

I checked similar questions but I couldn't figure out the underlying logic.
I am trying to add CornerRadius to a TextBox in a WPF project.
Here's what I tried so far:
In App.xaml I created a Style that I intend to reuse:
<Style x:Key="TextBoxStyle" TargetType="{x:Type TextBox}">
<Setter Property="Height" Value="27"/>
<Setter Property="Padding" Value="5.5"/>
<Setter Property="BorderThickness" Value="0"/>
</Style>
Adding: <Setter Property="Border.CornerRadius" Value="5"/> didn't work. However, the following worked, but with side effects (all borders where rounded):
<Style TargetType="{x:Type Border}">
<Setter Property="CornerRadius" Value="5"/>
</Style>
I want to keep the styles separate and basically use them like this:
<TextBox x:Name="ExampleTb" Style="{StaticResource TextBoxStyle}"/>
Can you please help me/ point me in the right direction?

It is actually very simple to achieve this, just follow these steps:
Step 1. Add a textbox to your window, right click on your textbox and select "Edit Template \ Edit a Copy..."
This will take you to the control template designer.
Step 2. Check this picture:
https://postimg.org/image/9h5ng8p9t/
P.S. I find blend better suited to design controls.

Trying to apply multiple styles to a DataGridRow

I have WPF application, i created DataGrid style in App.xaml to apply whole application.
App.xaml
<Style TargetType="DataGrid" x:Key="GridStyle1">
<Setter Property="HorizontalGridLinesBrush" Value="LightGray" />
<Setter Property="VerticalGridLinesBrush" Value="LightGray" />
<Setter Property="AlternatingRowBackground" Value="WhiteSmoke" />
<Setter Property="RowHeight" Value="30" />
<Setter Property="RowStyle">
<Setter.Value>
<Style TargetType="DataGridRow">
<Style.Triggers>
<Trigger Property="IsSelected" Value="True">
<Setter Property="Background" Value="Cyan" />
</Trigger>
</Style.Triggers>
</Style>
</Setter.Value>
</Setter>
</Style>
Then in window :
window1.xaml
<Style TargetType="DataGridRow" BasedOn="{StaticResource {x:Type DataGridRow}}">
<Setter Property="FontStyle" Value="Italic" />
</Style>
The problem that window style does not apply ( font style not italic )

It looks like you want to apply a global style to every DataGridRow in every DataGrid in multiple windows, and you also want to apply additional styling to DataGridRow in one or more DataGrids in one particular window.
If you've learned CSS before, you may expect stylesheets to be cumulative: In CSS, if you apply tr.style1 globally and tr.style2 locally, you get both, with tr.style2 winning the toss in any cases where they set the same attribute.
That's not how styles work in XAML. In XAML, an element may inherit styling from its parent, but it can have at most one Style of its own. Additionally, as you've found, Style has a BasedOn property. You can base one style on another, and get the cumulative effects of both.
Lastly, there are several ways to apply a style. You've found that you can apply them to every element of a given type in a given scope.
Unfortunately, because everything depends on context, the way XAML styles are applied can be very confusing at first (and at second, and sometimes third). Particularly when you are using one style (GridStyle1) to apply another style. It's not always obvious what overrides what.
It's best to keep things as simple as possible. We'll get rid of that RowStyle setter, because we don't need it. We'll just create a global DataGridRow Style that applies by default to every DataGridRow everywhere, and then we'll override that specifically in window1.xaml.
App.xaml
<Application.Resources>
<Style TargetType="DataGridRow" BasedOn="{StaticResource {x:Type DataGridRow}}">
<Setter Property="Background" Value="Cyan" />
</Style>
</Application.Resources>
window1.xaml
<Window.Resources>
<Style TargetType="DataGridRow" BasedOn="{StaticResource {x:Type DataGridRow}}">
<Setter Property="FontStyle" Value="Italic" />
</Style>
</Window.Resources>
That will apply to every DataGridRow in that window. The BasedOn attribute there will refer to whatever style has already been defined for DataGridRow in any containing context -- commonly, that means App.xaml, and if we don't add anything else, that'll be the case here.
The difference between this and what you had is that you were applying the Cyan Background style in a different way: The DataGridRow style you applied in App.xaml was applied via the RowStyle setter on your DataGrid style. That style was BasedOn WPF's pre-existing default Style for DataGridRow, and then it was forcibly applied to every DataGridRow in every DataGrid that used the GridStyle1 style.
The DataGridRow style you defined in window1.xaml would have applied, if DataGrid.RowStyle hadn't already been set in GridStyle1.
But as we've seen, you don't need to use RowStyle to apply a style globally to every DataGridRow. You can do that with the default style for that type, as in my App.xaml fragment above. DataGrid.RowStyle is useful for individually overriding the global DataGridRow style on one particular DataGrid. But you don't want to do that globally! So your styles in App.xaml should look like this:
App.xaml
<Style TargetType="DataGrid" x:Key="GridStyle1">
<Setter Property="HorizontalGridLinesBrush" Value="LightGray" />
<Setter Property="VerticalGridLinesBrush" Value="LightGray" />
<Setter Property="AlternatingRowBackground" Value="WhiteSmoke" />
<Setter Property="RowHeight" Value="30" />
</Style>
<Style TargetType="DataGridRow" BasedOn="{StaticResource {x:Type DataGridRow}}">
<Setter Property="Background" Value="Cyan" />
</Style>
And again, here's the Style in window1.xaml
<Style TargetType="DataGridRow" BasedOn="{StaticResource {x:Type DataGridRow}}">
<Setter Property="FontStyle" Value="Italic" />
</Style>
Extra Credit
The styles above should solve your problem.
But there are other ways to approach this stuff. Unless you're very comfortable with what we did above, what follows may just add confusion, so if you start reading this and you find that the more you read, the less you understand -- then stop reading! It can wait!
You could also make all text in a DataGrid be italic, but that changes the headers too so I don't think it's what you want:
<DataGrid
FontStyle="Italic"
/>
If you want to apply that Italic style on just one grid in window1.xaml, here's how to do that. If we add an x:Key attribute to a Style, it won't be applied to every DataGridRow in scope. Instead, it's just sitting there, waiting to be used by name as a StaticResource.
window1.xaml
<Window.Resources>
<Style x:Key="ItalicDataGridRowStyle"
TargetType="DataGridRow" BasedOn="{StaticResource {x:Type DataGridRow}}">
<Setter Property="FontStyle" Value="Italic" />
</Style>
</Window.Resources>
<-- ... -->
<!-- One grid with italic rows -->
<DataGrid
x:Name="dataGrid1"
RowStyle="{StaticResource ItalicDataGridRowStyle}"
/>
<!-- And another grid with default rows -->
<DataGrid
x:Name="dataGrid2"
/>
And here's another way to apply styling to the rows in just one grid in window1.xaml:
<!-- Yet another grid -->
<DataGrid
x:Name="dataGrid3"
>
<DataGrid.RowStyle>
<Style TargetType="DataGridRow" BasedOn="{StaticResource ItalicDataGridRowStyle}">
<Setter Property="FontWeight" Value="Bold" />
<Setter Property="Background" Value="Wheat" />
</Style>
</DataGrid.RowStyle>
</DataGrid>
Finally, you could have set RowStyle in GridStyle1, and then explicitly set RowStyle on specific grids in specific windows, as above. That would work. You could have also created a new DataGrid style in window1.xaml (based on GridStyle1) which set RowStyle to something else.

WPF Style at Windows or App level yields different results

I'm trying to learn Styling in WPF and encountered a funny thing:
There is a difference when I apply a style at application or (main) window level.
When I define the following resource in the App.xaml:
<Application.Resource>
<Style TargetType="{x:Type TextBlock}">
<Setter Property="FontStyle" Value="Italic" />
</Style>
<Style TargetType="{x:Type GroupBox}">
<Setter Property="FontWeight" Value="Bold" />
</Style>
<Application.Resource>
the GroupBox caption is bold and italic.
When I instead define the styling in the MainWindow.xaml:
<Window.Resources>
<Style TargetType="{x:Type TextBlock}">
<Setter Property="FontStyle" Value="Italic" />
</Style>
<Style TargetType="{x:Type GroupBox}">
<Setter Property="FontWeight" Value="Bold" />
</Style>
</Window.Resources>
The GroupBox caption box is only bold and not italic.
Can anybody explain this behavior?

In picking TextBlock you have unearthed something. TextBlock is not derived from Control, and thus behaves slightly differently.
See https://stackoverflow.com/a/27065140/4258144 :
there is a curious rule in WPF implicit styles are only inherited
across template boundaries by elements which inherit from the Control
class
I guess you can add to that, "unless it is globally specified in App.xaml".
UPDATE:
Following comments, here's a look at a GroupBox visual tree, taken from Snoop.

Why <Style TargetType="{x:Type Control}"> doesn't work? [duplicate]

I was just poking around a bit in WPF and wanted all elements on my Window to share the same margin.
I found that all Controls that are capable of having a margin derive from FrameworkElement so I tried the following:
<Window.Resources>
<Style TargetType="{x:Type FrameworkElement}">
<Setter Property="Margin" Value="10" />
</Style>
</Window.Resources>
And, this doesn't work.
I can apply this to all Buttons, but not to all Elements that derive from Button.
Am I missing something or is this simply not possible?
Am I the only one feeling like using CSS for WPF would have been a good idea?

Unfortunately, you cannot apply styles to the base FrameworkElement type; while WPF will let you write the style, it will not apply it to the controls that derive from it. It appears that this also applies to subtypes of FrameworkElement, e.g. ButtonBase, the supertype of Button/ToggleButton/RepeatButton.
You can still use inheritance, but you will have to use the explicit BasedOn syntax to apply it to the control types you want it to apply to.
<Window.Resources>
<Style TargetType="{x:Type FrameworkElement}">
<Setter Property="Margin" Value="10" />
</Style>
<Style TargetType="{x:Type Label}" BasedOn="{StaticResource {x:Type FrameworkElement}}" />
<Style TargetType="{x:Type TextBox}" BasedOn="{StaticResource {x:Type FrameworkElement}}" />
<Style TargetType="{x:Type Button}" BasedOn="{StaticResource {x:Type FrameworkElement}}" />
</Window.Resources>

The issue is that when searching for a style WPF does not search through all classes from which the current one derives. However you can give the style a key and apply it to all elements for which you wish to have a common property. If a property is specified in the style that cannot be applied to the element you are styling, it is ignored.

How do I know whether to use a style or override a control template?

This question is inspired by this recent question and other situations I've encountered in my WPF development. How do I know whether it is enough to set a style on a control to override some default behavior vs creating a new control template?
More concretely, in the question above, the author wants to change the look of a ListBoxItem when it is selected. (See code reprinted below). Everything works, except the Background property. How is one supposed to know that they should override the Control Template for this?
<Style TargetType="{x:Type ListBoxItem}">
<Setter Property="Content" Value="{Binding Path=Name}"/>
<Setter Property="Margin" Value="2"/>
<Style.Triggers>
<Trigger Property="IsSelected" Value="True">
<Setter Property="FontWeight" Value="Bold"/>
<Setter Property="FontSize" Value="18"/>
<Setter Property="Background" Value="Yellow"/>
<Setter Property="Foreground" Value="Red"/>
</Trigger>
</Style.Triggers>
</Style>

As to whether to use a style or template Ray provided a great response.
As to how to solve your problem without creating a template, maybe I can help.
The background color is being set by the SystemColors. Using Blend and creating a template you can see the exact xaml.
So if NO TEMPLATES! is a requirement you can always change what that resource is.
Example :
<ListBox>
<ListBox.Resources>
<SolidColorBrush x:Key="{x:Static SystemColors.HighlightBrushKey}"
Color="Yellow" />
<Style TargetType="{x:Type ListBoxItem}">
<Setter Property="Content" Value="{Binding Path=Name}"/>
<Setter Property="Margin" Value="2"/>
<Style.Triggers>
<Trigger Property="IsSelected" Value="True">
<Setter Property="FontWeight" Value="Bold"/>
<Setter Property="FontSize" Value="18"/>
<Setter Property="Foreground" Value="Red"/>
</Trigger>
</Style.Triggers>
</Style>
</ListBox.Resources>
<ListBoxItem>Test 1</ListBoxItem>
<ListBoxItem>Test 2</ListBoxItem>
<ListBoxItem>Test 3</ListBoxItem>
</ListBox>
That will give you the background color for that given ListBox and not screw up anything else in the app.

Styles can be thought of very closely to CSS styles in HTML. If all you want to do is change the basic properties of a control such as Background, Foreground or whatever properties it exposes then a Style is exactly what you need. Styles also allow you to apply triggers so for animations, a style is also sufficient.
If you're finding you want to change the intrinsice behaviours / inner workings on a control then a control template is what you want. For example, if you want to change how a button is laid out by adding some sort of grid behaviour, then using a control template is the way forward.

Unfortunately, for your specific example, you don't know unless you try it. Basically you first try it with a Style....and if that doesn't work for whatever reason, then you write a ControlTemplate. You usually only end up writing ControlTemplates for the reasons Ray mentioned.
My guess is that the trigger you're trying to set has also been hardcoded in the ControlTemplate...which is bad design imo because it prevents the Style from overriding it.

By "Background" I take it to mean the "blue" rectangle that surrounds the ListBoxItem when it is selected?
This is actually the FocusVisualStyle property, which is a style that describes what the item should look like when it is focused. The Control explicitly sets this property (described here), so in order to override it, you will have to redefine the Control Template, making sure to use a default Style setter to set it to {x:Null}.