Magic of some form is common to all types of ponies and many other creatures. However, professional magic users excepting alchemists are almost always unicorns, with occasional dragons and shadhavar. Reindeer, although unknown on the Isle of Yore and possibly extinct on post-Catastrophe Equus, are (or were) also capable of conscious magic.
Most unicorns have, apart from telekinesis and somewhat less frequently teleportation, magic related only to their special talent. Unicorns with broader magical aptitude often become professional magi. Historically, numerous titles have been applied to professional magic uses, including titles of nobility. "Mage" or "magician" translates the current general term on the Isle of Yore. "Archmage," originally a title with specific legal meaning, has become somewhat diluted to refer to any very powerful mage. A wizard is a scientist who studies magic as a profession and is usually but not necessarily a highly skilled magic user, the term "hedge wizard" refers to a rustic village mage with implications of pretentious behavior. "Hedge magic" and "hedge mage" have no such implications of pretension. Industrial and agricultural magicians continue to be the most numerous category of magic using professionals; their education is much narrower than that of trained generalists, but it is not limited to their special talent.
Professional magic users are generally trained at magic colleges, or, especially in the case of hedge mages, by apprenticeship.