The venom symbiote in this continuity works mainly the same way as normal, it attaches to someone (in this timeline Peter’s boyfriend) and acts like a parasite to their mind. Peter’s boyfriend for the most part actually manages to have a surprising amount of control over it though.

The carnage symbiote basically acts as a parallel to venom, instead of infecting the host’s mind it infects and consumes their body to the point where they basically become one with Carnage.