No, they mean the same, but "worry about" is a lot more common. I almost always use 'worry about' myself.

Worry over” is a bit more dated and probably an expression you’d only find in a book now. To say that you “worry about” something is much more common in everyday speaking. Occasionally you might also say to someone: “Don’t worry yourself over nothing!” or “You’re worrying yourself over nothing!” but the word “over” is completely interchangeable with “about” and is both subjective and a matter of personal preference - both are grammatically correct.

I wouldn't say so! I'm a native English speaker and to me they have the same exact meaning. I'd say 'worry about' seems a bit more natural out of the two :)