For layer lists and state list i think the equivalent is VisualStates but they are not so similar. Define different visual states for a control, You can find many different examples to VisualState's here inside a VisualState you gave different properties different values (such as different Image to background of a button when pressed) or define animations.
For shapes there are classes that you can define in your xaml file. If you want to define a gradient should look at brushes.