Non-captured pets, such as those obtained as rare drops or purchases, have rarities based on how they were obtained and how difficult they were to obtain. Currently this is not visible in the basic interface. It is believed their rarity will be added to their information in a future update.
For now I recommend getting the Pet Battle Quality Glow Addon (LINK
). Its primary purpose is to show the rarity of pets you encounter in the wild, but it also shows the rarity of the pets you bring into battle; download the Addon, enter a random battle with your Strider, and its rarity should be depicted by the color of the pet's name and the glow around its icon.