Raised pets
A raised pet has its own level, EXP, HP and lives. Its tooltip shows the bonus it grants. Read those values before choosing a pet; appearance alone does not describe its contribution to your build.
Perfect pets
A pet’s tooltip can include level bonuses and additional effects. The illustrated pet is an individual example, not the base stats of every pet of that appearance. Compare its actual tooltip with your current pet.
Pickup pets
Pickup pets serve a different role from raised pets. Their equipment reference lists the available families and effects. Use the Pet Filter window to inspect collection preferences rather than assuming a pickup pet and a raised pet have the same functions.