Carnage is Venom’s offspring.
Carnage has never, as far as I know, had a host other than Cletus Kasady.
Venom has had multiple hosts - Eddie Brock (currently ANTI-Venom, who is a spikey, colour-inverted version of Venom), Eddie’s ex-wife, Amy, another woman named Patricia Robinson, a mafioso named Angelo Fortunado, and currently, Mac Gargan (formerly known as the Scorpion). I’m not familiar with the Robinson or Fortunato versions.
Carnage is also a flat-out villain, all the time (since Kasady is a complete psychopath), whereas Venom has been both a villain and an anti-hero, often with the same hosts. Anti-Venom is an anti-hero, while Gargan-Venom is a villain (posing as a hero).
Venom is always black/blue/blue-black with a white spider-symbol. His basic look beyond that changes depending on the host, and, for Eddie, what point in continuity it is - at its most basic, Venom looks like his host in the black spider-man costume. But all of his hosts - except Spidey, and apparently Fortunado - have had toothy mouths with prehensile tongues. Brock and Gargan, the symbiote tends to bulk them up, severely, especially during the mid-90s, in Brock’s case. The extent of the mouth/tongue also changes - at its most extreme, it bears no connection whatsoever to the host’s underlying anatomy. The eyes of the costume also change.
Carnage is way more consistent - he’s always black and red, he’s always skinny (like Kasady), and he has the teeth, but not the tongue.
It’s probably best not to go into Carnage’s offspring. Especially since I really don’t know much about them.