The back story of Carnage and Venom is quite complex. Both originated from the symbiote species. Venom was the first to bond with a human host, and Carnage emerged as a more violent and unstable offshoot.
In the comics, the outcome of their battles varies. Sometimes Venom emerges victorious and kills Carnage, but there are also instances where Carnage escapes or the fight ends inconclusively.
Well, it happened when the symbiote found Cletus Kasady. This combination of a powerful symbiote and a deranged mind gave birth to Carnage. The symbiote's influence amplified Kasady's evil tendencies, making him a truly terrifying force.