There are two types of Plush, Magic and non-Magic. Magic Plush can be used on a villager to change their species and color. Afterwards, the magic plush turns into a normal plush.
Some certain colors can only be obtained by using a magic plush, such as the Magic Archer Raptor Plush. These special plushes can be obtained by certain events like the Snow Festival, bought in the Quest Shop and the FurDollar Emporium, dropped by monsters, or by exploration events. These plushes are often limited and most will retire after their respective events ended.