Originally Posted by
Ratman
In the Throne, the individual 'character' is a bunch of data which can be turned a lot of things, for example manifest as a Counter Guardian. There is also, seemingly, an absolutely minimal file of how the record has been used, which is referenced when it's reused, which can result in the Servant being aware of a previous summon, but usually doesn't.
The Fuyuki Grail system interprets that bundle of data into whatever works, which can be a few different classes, and adds a bunch of pre-determined data like modern language. For Diarmuid, that original bundle has him as a swordsman and a spearman, but in a Grail War he can only be one of those, so the Grail picks one and discards the rest of the record. Their personality can end up being something more fit to what they were like in respect to using those weapons/tools/skills.
In case of Extra this doesn't matter because literally your mom can be a servant in the Moon Cell.
In FGO this doesn't matter because that bunch of data they've originally downloaded, which maybe vaguely looks like what's in the Throne, can be 'enhanced' with complete nonsense from Lostbelts or Singularities, or create fresh records of people who aren't in the throne at all, like Kiara, or even things that have absolutely no business being Servants, like Foreigners.
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Lancer Artoria is in London, which has a bunch of other issues. You could say don't think about it too hard, but you could also say she's King Arthur summoned as the King of the Wild Hunt, and given Ron because there's no reason she can't have it instead of Excalibur if the summoning mechanism thinks it's a good idea. It's present in the record.
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Okita Alter is also a joke character down to her being a Counter Guardian. Why is she an Alterego? Who knows? Why can a servant at all outright be summoned as Alter when the first and only case of it we have seen is Saber falling into the curse pool, which is how she turned into someone she never was in reality? Don't think about it too hard.