The home planet pets are more aimed towards companionship while the space monster pets are more suited for combat. In addition to Starter Pets the player can tame many types of animals and monsters. Capture pods can be crafted at the Creature Capture Station. Before you can capture pets, first you need a capture pod. Home planet pets are more suited for companionship and following you around, while the space monsters are more for combat purposes, so it's up to you which types of pets you want to go for.