How are quasars and supernovae different?
A supernova is an event and a quasar is an object.
A supernova is a violent release of energy in the last stages in the life cycle of a massive star. Essentially a giant explosion.
A quasar is a super massive disc of all the material that has gone into orbit around a black hole. Usually when we think of black holes we think they pull everything into them. This is true up to a point. Any objects further away than that limit (called the event horizon) actually go into orbit around the black hole. For larger black holes a lot of objects can end up in orbit forming a disc of material (called an accretion disc). Once enough material is trapped in the accretion disc we start referring to it as a quasar, and it can have so much material that it can get a trillion times brighter than our sun.