How to delete animation from only 1 object in this case (object created by separate selection)?

(Suggestions to improve the title are also welcome)
Can you please help me understand this behavior:

Case “normal”
animate an object
duplicate it

  • both objects perform the same animation.
  • using “clear keyframes” on one of these objects removes the animation from this object only

Case “why”
animate an object
in Edit Mode, select some part of the object, Separate Selection

  • both objects perform the same animation.
  • using “clear keyframes” on one of these objects removes the animation from both(!) objects

Why does this happen and how do I remove the animation from just one object in the latter case?

When using separate selection:

  • in 2.79, 2.81a, 2.82a
    the animation action data-block is linked to the new object that was created by Separate Selection. Therefore deleting keyframes of one object also deletes them on the other object. Solution: make single-user copy of the Action data-block in the Action editor. Now unlink the action or delete the keyframes.

  • in 2.83
    the animation action is copied to the new object. No problem here.