What is the difference between an Animator and an Animation?

Animations are older versions of Animators. Animators where introduced in 3.0 to help overcome some short-coming that Animations have.

Animations only change the visual representation of an object. This is fine if you're just changing opacity, but it causes issues when you translate, rotate, or scale objects. In the old days before Animators, if you translated the object, you had to perform a re-layout with the new coordinates. It could be rather difficult depending on where the object moved.

Animators on the other hand change the physical properties of the objects. This means that if you move a View to a new location, the touch coordinates will be mapped at the new location without any other intervention.

Personally, I don't use Animations much anymore unless I'm developing at API's 2.3 or less. Thankfully that's becoming less of an issue. There are also some old classes that still use Animations API especially when it comes to using xml resources such as the android.support.v4.app.FragmentTransaction class (the normal FragmentTransaction supports Animators instead).

As a side note, the project NineOldAndroids was developed to mimic functionality of Animators but using Animations so you can make apps that work all the way to 1.6.

An Animation object animate the view's image. If you use this for example, to move a button around the screen you will not be able to click on it at the new visible position because it was not truly moved, but only his bitmap representation was translated. You will also not be able to change the proportions of it since you are making modifications to a bitmap. If you use xml files, place them at anim folder.

An Animator object animate the view's property (like the margin or width). If you use this to move a button around the screen you will be able to capture clicks on it in the new visible positions. If you use xml files, place them at animator folder.

If you only need cosmetic effects, like fade in or small appearance translation, using a Animation will be more efficient because it does not call layout() or measure() methods. If you do need to capture actions like click events, use a Animator.