Question

What’s the difference between the two, when should RegisterAttached() be used instead of .Register()?

Answer 1

I assume you meant DependencyProperty.Register and DependencyProperty.RegisterAttached.

DependencyProperty.Register is used to register normal DependencyProperty. You can see those as just regular properties, with the added twist that they can take part in WPF’s DataBinding, animations etc.
In fact, they are exposed as normal property (with the get and set accessors) on top of the untyped DependencyObject.SetValue / GetValue.
You declare those as part of your type.

Attached properties on the other hand are different. They are meant as an extensibility system. If you have ever used Extenders in Windows Forms, they are kind of similar.
You declare them as part of a type, to be used on another type.

They are used a lot for layout-related information. For example, Canvas needs Left/Top coordinates, Grid needs a Row and a Column, DockPanel needs a Dock information etc. It would be a mess if all of this had to be declared on every Control that can be layouted. So they are declared on the corresponding panel, but used on any Control.

You can use the same thing to attach any information to a DependencyObject if you need to. It can come in handy to just declare a piece of information that you can set in xaml just to be used later in a style for an existing class for example.

So those two kind of DependencyProperty serve a very different purpose. Regular properties (registered through Register() ) are used just like normal properties as part of the interface of your type. Attached properties (registered through RegisterAttached() ) are used as an extensibility point on existing classes.

Hope that clarifies it a bit.