As described in point 6 of http://mathoverflow.net/tips, the star icon is for favoriting questions so that you can return to them conveniently - the number you see underneath the star is the number of people who have favorited it so far. Certainly, one may want to bookmark a question but not vote it up, or vice versa, so these aspects are disjoint. Also, there are separate badges for having a question which is favorited 25 times, and for 100 times.
One difference I have since learned is that I can favorite my own question with a star but I cannot upvote it. Also I can downvote but I don't know how to downfavorite. Can everyone who can vote also favorite? Are those the only differences between stars and votes?
There's no downfavorite - it's binary, i.e. either you've favorited a question or you haven't (clicking the star once favorites a question, clicking it again undoes it). Although you will always have available to you a list of the questions you've asked, I suppose there may be some of your questions which you were particularly interested in, and others which were idle curiosity - being able to favorite your own questions lets you make a distinction. However, voting yourself up (and thereby giving yourself reputation) would be unethical, and even if it were set up so that self-votes didn't increase reputation, I think it would be uninformative - presumably, everyone thinks their questions are good and would vote themselves up, and we may as well start all questions at 1 vote. Users with reputation >= 15 can upvote, users with reputation >= 100 can downvote, while I believe a user of any reputation can favorite (because favoriting a question doesn't affect the reputation of the asker). That's all I can think of on the topic of voting vs. favoriting at the moment - hope it's helpful!
Zev Chonoles, thanks now I understand how it works! But I think that if you favorite your own question that should not appear in the publicly-visible count.