"Any" means "at least one". It implies you don't care which person/thing. "Anyone" and "anybody" (there's no difference between them) means "any person". "Anything" means, well, "any thing".

"Some" (along with "someone" and "something") refers to something specific. "Someone" and "somebody" (again, there's no difference between them) means "some person".

If you're looking for anyone, you're looking for <em>any </em>person you might come across. You probably don't care who it is.

If you're looking for someone, you're looking for a specific person. You might not even know who that person is yet, but no one else will suffice.

If you need help, you might shout out "Is anyone there?". If you hear a noise behind you, you might shout out "Is someone there?".

Statistically speaking, "any" is more common in negative sentences and questions, and "some" is more common in statements, but don't let anyone tell you that grammar states that that's how they must be used, or that the only difference between them is grammar. They are different words with different meanings. It's useful to know that if you're asking a question you should <em>probably</em> use "any", but if you remember it as a rule and ignore the actual meanings of "any" and "some", it will only hurt your English.