If you're chipping (or putting) from off the green, and your ball hits a ball on the green, then you play your ball as it lies, and the other ball is replaced to the original position. And there is no penalty. That one is easy.
But if you're putting, then this is covered by the Exception in Rule 11.1a (2019 version) which states:
Exception – Ball Played on Putting Green in Stroke Play: If the player’s ball in motion hits another ball at rest on the putting green and both balls were on the putting green before the stroke, the player gets the general penalty (two penalty strokes).The penalty is on the player who hit the putt. Presumably the other ball is replaced to its original position.
So I advise you to ask the other player to mark his ball if it's anywhere near the line of your putt.
Another interesting part of Rule 11 (2019 version) is 11.3, which says that you can't move any object that may affect a ball in motion. The exceptions to this rule include the flagstick, equipment, or another ball. So if someone's putt (including your own) looks like it may hit one of those three objects, then you can move the object.
This gets into the realm of the recent "backstopping" controversy on the LPGA. As far as I read the rule, if your opponents putt is coming in way too hot, and your wedge is laying off the green between the ball and a bunker, you can move your wedge, allowing your opponents ball to go into the bunker. Or if you like your opponent, you can leave it there and stop the ball.
Interesting....
