Small Cat and Big cat is same ?

Oh, yes, pumas will eat domestic cats.

No it would only kill the cat if it was starving or the cat was an easy kill in comparison to what else was on offer but usually cats will only eat prey not other predators. Maybe the high based cereal diets most cats are on it smells it as a predator. Only if the cat acted rude or aggressive, even then it probably would not kill it but just smack it a couple of times but that may kill a domestic cat. Peoples pets generally get taken because housing or farmland is put through their territory OR due to overhunting they don't have enough food so have to hunt pets or livestock.

No they are not the same, domesticated cats have more in common with lions or cats that live in groups.

Stray cats form prides (?) to some extent, families will stay together usually if left especially female family members.

Pumas generally live in solitude apart from when breeding and raising cubs.

Um, yes? There are domestic cats that will treat each other as predator and prey, I wouldn't even MESS with something like this.