The ones that look like ordinary housecats are naturally incredibly gifted with magic. Like, more powerful than Altmer. There are horror stories from people who tried to invade Elsweyr only to discover fireballs raining down on them from the highest branches of the trees, where even Bosmer can’t climb. Those really big ones meanwhile are referred to as “battlecats” and carry other warriors into combat. Every single one of them has at least human level intelligence.
And yeah which one you’re born as depends on the phases of the moons when you’re born, so a family will usually be a random scattering of types. Kind of like how the birthsigns work, except instead of ‘you run a little faster’ or ‘you have a little more magic’ the result is ‘you grow up to be a fucking tiger’.
There are reasons I really want the next elder scrolls game to be set in Elsweyr.