What do the stars represent on the sylesties

it depend of the color of the star and it's location tho you are probably speaking of the yellow and blue stars in the genetic section.

A gold/yellow star mean that this pet is a tagged from a themme, those are specific pets with selected color pallet. Those can only be exclusive or wild pets. Here is an exemple of an Imperial Dragon Ny'vene, this themme was avalable during a festival two years ago.


A blue star mean that this pet is a pure breed or pb for short, to be pb a pet nead to have their two parents sharing the same themme, it don't matter if the parents themself are pb as long as they are all from said themme. By exemple this is a Lightning Struck Ny'vene pure breed, all her encestors are pb or tagged from the lightning struck themme. ^-^

Technically speaking the number of stars represents 'difficulty' of the fight. This guide page goes over the stars