If you admire someone you regard them with respect and approval. 'Look up to' is more than just 'admire', and it is more personal. You might look up to an older relative or colleague, in the sense that you see them as a kind of role model. If you look up to someone you aspire to be like them.

Also admire can be used for specific parts of someone's personality as well as generally e.g. you might admire someone's sporting ability, dress sense, music taste etc whereas if you look up to someone it is much more about their character and behaviour as a whole.

"admire" can be used in other ways but in this sense there's not much difference. "look up to" means to admire and respect but "admire" itself has the meaning of "respect" in it. The only slight difference is who it's used with. "look up to" is usually with people you know and they are usually older than you, but not necessarily.

I agree with the above comment. To look up to somebody it is usual to know them personally. You can admire lots of different types of people, for example you might admire a celebrity such as a musician, sportsman or actor but it would be strange in my opinion to say you look up to these types of people. Looking up to is used for a person older than you, it might be a parent, an older sibling or cousin etc and you think of them as a role model.

They are synonyms.