I think that the main distinguishment is whether or not the other person welcomes/shares the feelings. I've thought i was in love with a close friend before. I obsessed over making him happy, getting his approval. I felt jealous when he talked excessively to other people. Id say that, maybe in a lesser degree, these are traits of people in a normal relationship, but because he did not share these feelings i was called "obsessed". I have the same feelings for my current boyfriend, but with much less anger i suppose. In this relationship the only time the word "obsessed" has been used to describe me is to say that I'm obsessed with his happiness, more of a joke really.

So, to me, unrequited love is what people call obsession.