...Eh...what part of "Final Fantasy V had both Mystic Knight AND a Red Mage and the Red Mage we have is pretty faithful to Final Fantasy V's Red Mage." do you not understand?! Final Fantasy V is the original game in which Mystic Knight first appeared. That is the game which made its identity. It was a single player game so it was devoid of all the crap that MMO's have to deal with for the sake of balance and what not as well. If you're looking at a class identity...look at the source.
Or maybe now you want to say that our Red Mage is also kinda similar to an Onion Knight because the skill Embolden, originating in FFXI (it was never a skill in single player game), is used by Onion Knight Refia in Final Fantasy Brave Exvius?!
Also, Red Mage NEVER was in any way similar to Mystic Knight in any single player game. I don't know about Final Fantasy XI, I admit, but I do know that it was a game with a pretty "free" interpretation of certain jobs. It is by no means an argument to say that "This or that class have this or that skill set.", especially since every single other game in existence, before and after it, blatantly says to the contrary.
Doesn't matter. Most jobs in this game generate mana. That doesn't make all of them Red Mages or Mystic Knights. It's not about how mana is generated, it's about how it is used.
Red Mages are born from time when Black Magic and White Magic users "buried their hatchet" and joined forces, teaching each other their art, thus making it possible for a single person to use both kinds of magic. Seeing as spells leave aetheric residue whose nature is based on what spell was used (you know, the core point of a lot of stories, including several plot points), it's only reasonable to assume that the black and white mana that Red Mages accumulate is simply that. A balance of black and white aetheric residue that they store in their crystal and combine, able to utilize it to strengthen their rapier.
Really, it's not that hard.
No...Red Mage in FFXIV never, ever casts a spell on its rapier. NEVER. He strengthens its rapier with mana, yes. But a Mystic Knight is about passing spells effect onto the sword. There is no spell effect on Red Mages rapier. How many times do I have to explain it before you realize that the difference between "Cast a spell on a weapon then use the weapon to attack with both the blade and the spell." and "Make the weapon hurt more with magic." is the entire reason behind this discussion. Coating a weapon in some sort of energy is a fundamental high-fantasy technique. Warriors do it, Paladins do it, Dark Knights do it, Samurais do it, Bards do it, Monks do it, Dragoons do it...Every single physical job does it. The specific energy varies. But the idea is there. Mystic Knight does not coat their weapons with energy. It gives the weapon a specific, additional effect, that does not need to be damage either, since it is an entire, capable spell.
Anyway...that is all. I won't even bother answering to the guy that clearly doesn't give a darn about the lore of the game either. It's just not worth the time. Believe what you will.