There are a bunch of different words for groups depending on what kind of animal and how they organize.
Canines are packs because of the way their dominance structure works, the high degree of mutualism (the way the needs of the group are treated as more important than the interests of particular individuals within the group), the way they form teams in hunting, and the minimal gender-dependency of roles within the group - a female is nearly as likely to be the “alpha” as a male, and females and males have basically the same role in hunting.
Cats (Lions in particular) on the other hand are “prides” - which means they tend to hunt solo, share food only with close kin, and share territory with other members of the pride. And that applies mainly to the females. Aside from one or two males that are more or less wholly owned (and shared) by the lionesses of the pride, males are only loosely associated with any particular group and wander around a lot. And if a female wants to boink one of them and spend a year raising a set of cubs with him that have no relation to the pride males, the pride males don’t get a say in that. Prides work very differently than packs.