They have distinct meanings when used to make comparisons. If someone or something "looks like" someone or something else, they are alike in appearance. "You can't use "seems like" to convey that meaning. "Seems like" tells us that the similarities involve some other quality or qualities besides physical resemblance. The only time they're exactly the same in meaning is if we say "It seems like" or It looks like" when we're expressing an opinion, judgement, reaction, etc.

They are not the same because "seeming" conveys judgement whereas "looking" reflects appearance. The difference is important because when you say that something "seems" a certain way, you also open up the possibility that it might not actually be that way. So, "he seems like a good boy" sounds like you think he is a good boy but you are not certain. If you were certain he was a good boy, you would just say "he is a good boy". However, "he looks like a good boy" contains no such ambiguity unless your intonation of "looks" makes it sound like you have doubts. For another example, look at this quote from Shakespeare, "Julius Caesar": "It seems to me most strange that men should fear; Seeing that death, a necessary end, Will come when it will come." "Looks" would be grammatically correct but it would not convey that the person is thinking, not totally certain, and making a judgement.

Yes, many. It looks like rain. (Rain is predicted. I expect it) It seems like rain. (Doesn’t have a clear meaning without context)