Ok let's make a few things clear from the last 3 posts:
The original black costume was the Venom symbiote but after Spider-man got rid of the symbiote suit he liked the black suit enough to make a similar one out of cloth. He continued using that one until the suit returned with Eddie Brock, calling itself Venom. Peter was so disgusted, and Mary Jane was so scared of the look of the black costume, he decided to return to his original blue and red costume.
Carnage is actually its own symbiote. It was the offspring of Venom and it joined with Cletus Kassidy in prison to make Carnage.
Now, that was the original Marvel Universe of Venom and Carnage. The Ultimate Marvel Universe (where the new game is set) story goes like this:
The fathers of Peter Parker and Eddie Brock Jr. made a suit/compound that they hoped would cure cancer but never got a chance to finish creating it. Years later, Peter and Eddie Jr. got in touch again and Eddie Jr. showed Peter a leftover part of the suit. Peter came back as Spider-man one night and accidently got some on himself and it turned into a suit. He wore it for a little while until he realized that it was turning him ultra violent so he removed the suit from himself and destroyed the sample. Unfortunetly he told Eddie Jr. about the suit so Eddie used the other sample he had (which Peter didn't know about) to turn himself into Venom.
As far as Ultimate Carnage, I read the entire arc for it but I'm still not exactly sure how it went, it was slightly confusing. It basically had to do with a scientist, Ben Reilly, growing a clone out of Peter's blood which apparently still had the venom suit in it. I can't remember how it exactly went.
