if i was obsessive i would call u 100 x's a day and stalk you.
if i was possessive i would make u wear what i want u to wear, make u do what i want u to do and try to control everything you do.
Obsessive is when you can't stop thinking about something, talking about it/them and your whole world revolves around whatever/whoever it is. Possessive is when you don't want people playing with your toys or talking to your partner. Their possessions or friends and family are theirs and they don't want to share.
Obsessive means you cannot stop thinking about them 24/7.
Possessive means you really want them to be yours, and will not let anyone else even talk to them etc because you are worried someone will take the person away.