How do I copy an animation from one rig and apply it to another?

Support Animation and Rigging
#1

They’re the same rig, just with a different model.

#2

Since you didn’t attach anything, I assume that you have an action with the old rig. Append in your action to the blend with the new rig. Select the new rig. Make sure the action is then selected in the dope sheet and it should work for you.