Difference between TargetType="controlType" and TargetType="{x:Type controlType}"

Nothing. Since the property type is Type, the XAML parser knows to try and convert whatever you supply to a Type. In other scenarios, the property type might be less specific (eg. Object), and that's where you need the markup extension, otherwise the XAML parser will just interpret your value as a String.

I have recently encountered a situation which shows that x:Type is different from TypeName-as-String.

From my experience -

x:Type considers the strong name or the version of the assembly but not TypeName-as-String.

I have explained about my scenario and other details in my blog here -

Importance of specifying AncestorType with x:Type in RelativeSourceBinding

Apart from this, there is also difference in how WPF infers the type. For x:Type TypeExtension is used, whereas for TypeName-as-String FrameworkElementFactory is used.

As per MSDN - x:Type Markup Extension

Type Properties That Support Typename-as-String

WPF supports techniques that enable specifying the value of some properties of type Type without requiring an x:Type markup extension usage. Instead, you can specify the value as a string that names the type. Examples of this are ControlTemplate.TargetType and Style.TargetType. Support for this behavior is not provided through either type converters or markup extensions. Instead, this is a deferral behavior implemented through FrameworkElementFactory.