These are a defining and a non-defining relative clause :-
(A) He deleted the picture that upset me.
(B) He deleted the picture, which upset me.
Could you please explain the difference in meaning of these sentences?
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You can replace ", which..." with ", and it..."
So the second becomes "He deleted the picture, and it upset me". This reveals the ambiguity. The "it" could refer to the picture, but it could also refer to the deletion (the second interpretation is more likely)
The first is not ambiguous, the relative clause describes the picture.
(A) He deleted the picture that upset me. (B) He deleted the picture, which upset me.
The first means that there is an upsetting picture and he deleted it. No indication of how I feel about the action.
The second means that the act of deletion upset me. No indication of how I felt about the picture.
The comma is doing some work here too. Removing it from the second moves it a lot closer to the meaning of the first, because "that" and "which" get swapped with each other all the time. Not saying that's a good thing or a bad thing.
The opposite - adding the comma into the first - doesn't quite work as well without help. It would require something else to move completely to the second meaning. Maybe this would be enough to move the upset to the act and away from the picture: "He deleted the picture, and that upset me."