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Spiderman is Peter Parker. He's a hero. (When the symbiote attaches itself to him, he becomes Black Spiderman. The symbiote increases feelings of power and rage, so when he wears the suit it makes him feel more powerful, but it also makes him meaner.)
Venom is Eddie Brock. He was a rival of Peter Parkers, and when the symbiote attaches itself to him, he becomes Venom. He's a villian.
Carnage is Cletus Kassady. He was a serial killer who was in prison with Eddie Brock and when the symbiote attaches itself to him, he becomes Carnage. He's a villian.
The symbiote is the alien lifeform Spiderman inadvertantly brought back after "The Secret Wars" comic arc.
edit***
In the comics Carnage and Venom would team up to fight Spiderman. Now there have been many differnt story lines and origins, but most likely than not Venom and Carnage were teaming up against Spidey.