What happens if you lift your opponents ball on the green, and mark it, thinking that it was your ball?
If you're lifting it to identify it, then it is clearly okay, and no penalty. Just replace the ball (Rule #7.2).
If you were searching for a ball and moved it, then there is no penalty (Rule #7.4).
As far as I can tell, in stroke play, you are an outside influence for another player's ball, so there is no penalty (Rule #9.6). Replace the ball and continue.
In match play, it is a one stroke penalty to deliberately touch your opponents ball, But there is an exception to the rule if you are on the putting green and believe it to be your ball (Rule #9.5b Exception 1). So no penalty there.
