ONE OF THE HORSEMEN… WERE COOKED!! | Fate/Strange Fake Ep 12 Reaction

THE MOST IMPORTANT CONTEXT HERE (non-spoiler):

Magician and Magus/Mage means two entirely different things in this world.

Mages are what you normally see in the series, the modern mages: Rin, Shirou, Flat, Waver etc. and they use "magecraft".

Magicians use "True Magic" which is borderline divine. Quite literally creating miracles out of nothing.

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So far, there are only 5 Magicians/True Magics ever to exist outside the age of mystics. And we've been shown three so far in anime.

2nd Magic, Kaleidoscope: Transportation, Manipulation, and Observation of multiple parallel universes and drawing unlimited mana from them (You can see the user, "an old man in a chair in a room of crazy visuals" at the end credits in Fate/Strange Fake: Whispers of Dawn).

3rd Magic, Heaven's Feel: True Immortality, Unlimited mana, and the Materialization of the Soul. (Heaven's feel movies)

5th Magic, Magic Blue: Time Cheat. Sending mana costs in the future, granting practically unlimited mana. Time manipulation, heat, and entropy. (Upcoming Witch of the Holy Night anime and the Tsukihime series)
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Now. By asking Mr. Black that she wants to be a "Magician". She's basically asking for the holy grail, because a wish of that magnitude requires the holy grail.

and, in essence, she quite literally asked Mr. Black to win the Holy Grail War. And this made Mr. Black physically manifest his true form or his true name, "The Pale Rider".

Now, The Pale Rider has joined the fight seriously and is dead set on winning the war.