Different qualities aren't limited only to wild pets—many rare World drops and special non-wild companions have had their stats boosted. For example, the world-drop dragon whelps (Azure Whelpling, Crimson Whelpling, Dark Whelpling, and Emerald Whelpling) are of [rare] quality. Check your Pet Journal to see the color-coded rarity of your non-wild pets.
The original World of Warcraft was released in 2004, and World of Warcraft Classic aims to recreate the state of the MMORPG before its first expansion, The Burning Crusade, was rolled out in January 2007. Previously, players looking for a “vanilla” version of the game were only able to experience it on custom servers such as Nostalrius, which Blizzard shut down in 2016 to protect its intellectual property.