Up and down. Two words that we generally think of opposites, but in actual use they are quite different.
This became apparent yesterday, when I was in the meeting and the organizers said, “Let's wait a few minutes for others to turn up”, and I realized that “turn up” is not the opposite of “turn down”. The latter means “to reject or refuse”, and the former refers to the biennial flowering plant Brassica rapa var. rapifera.
We came up with a number of other examples of this phenomena. Here's the full list