I Can, I Can't (-ㄹ 수 있어요)

수 literally means “a way” or “a method.” -(으)ㄹ 수 있다/없다 reads as “there is/isn’t a way to do this,” a broader statement about capability. 못 is punchier and tied to one specific moment: 수영을 못 해요 fits an immediate obstacle, while 수영을 할 수 없어요 can describe a standing inability, like never having learned at all.

~ㄹ 수 있어요? is the standard way to ask about someone’s skills, the Korean equivalent of “can you speak English?” or “can you drive?” It’s asking about general ability, not permission or a one-off circumstance.