Pet Battle Families
Here you can see which pet families are strong and weak against other pet families, as well as the passive bonuses for each family type. For example, Aquatics receive a 50% damage increase (base dmg x1.5) against Elementals while suffering a 33% damage penalty (base dmg x0.66) against Magic pets.
Some will have abilities which don’t fall under the family group, such as a Humanoid with Flying or Magic abilities. In some cases, a varied list of abilities may improve your chances at defeating a tougher opponent.