Minor pet

Minor pets are small collectible animals, which include lizards, snakes, rodents, turtles, small birds, and large birds. Minor pets are featured in The Sims 3: Pets and The Sims 4: My First Pet Stuff. In The Sims 3: Pets Common minor pets can be purchased, while rarer pets must be caught in the wild. Minor pets can be set free if a Sim cannot properly care for them. If kept in a Sim's inventory for too long, minor pets can escape. Birds can be killed by cats when they're placed on bird cage or bird tree. Unlike the main pets, these pets can be spotted by the Collection Helper lifetime reward.

Minor pets should be kept in their respective terrariums/habitats/cages. Their values increase over time. While being kept in the terrarium, they need to be fed regularly and played with in order to keep their longevity. Otherwise, they will eventually die.

Large wild birds can only be acquired by befriending them. Sims have a hidden Wildlife Skill, which determines whether befriending interactions are successful. All birds can be taught to talk and sing by Sims. Cats can be trained to hunt minor pets, excluding large birds. Some minor pets require minimum pet hunting skill before they can be caught.

In The Sims 4: My First Pet, they're reintroduced but only featuring rodents such as: Hamsters, Rats, Hedgehog, and a new rodent, Miniature Bubalus Voidcritter.

Rodents
Although they are referred to as rodents in-game, shrews and hedgehogs are not actually rodents.