Well, pets are usually for community events like Easter, Halloween, and Christmas and appear during those months (like the chicks, bumblebee and rabbit around Easter, the ghost, the cat and bat around Halloween, penguin and little snowballs during Christmas, Wibbit was I believe somewhere during summer) They are more seasonal things found within the month a seasonal holiday takes place.

Whilst at first there was only one per event, there have been a few added in upcoming years since it started. Bumbee, Clover and Peepers for spring/Easter, Wibbit for summer, Batty, Ender and Speck for autumn/Halloween and Topper and Powder Poofs for winter/Christmas. When those events take place they can pop up pretty much everywhere on the pmc site

The pets stay the same each year, there is a different pet for each month that has a pet, not all of them do, and as far as I know pets can be found anywhere besides a user profile, if you see one there, that is that user's pet.