1. to look like <someone or something>. A noun or pronoun (why?). Mary looks like Joanne.
2. to seem <adjective>. Mary seems happy. The situation seems desperate.
3. It seems that <clause>. It seems that he has run away.
4. It looks as though/as if <clause> It looks as though he has painted himself red.
In addition to the slight differences in grammatical context, as above, you should probably say "looks like" for a physical appearance, and "seems" for a state of mind or for any abstract circumstances. See my examples. But that is not an unbreakable rule; in (3) and (4) "look" and "seem" are basically identical. To say "seem" is a little more formal.
Instead of "seem", you can say "appear" in all these examples, with the same connecting words. "Appear" is even more formal.
PS. For (2): "to seem [to be] <noun>" is also possible. He seems to be a good man. He seems a good man. For (1) and (2) the distinction between the physical and abstract is quite strong, I think.
Student or Learner