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.