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The great debate: Spells Slots vs. Magic Points
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Tabletop, DnD, board games, and minecraft. Also Animal Crossing.
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Rules
Honestly my favorite is the way GURPS handles it by default, where each spell such as "Create Air" or "Control Air" or "Locate Object" is a skill. You know the spell, you can cast the spell whenever and however you want, and there's no hard restrictions on who gets magic unless your GM says so. To balance this freedom, each spell is expensive points-wise and is hyper-specific, and usually you have to have the Magery advantage to do magic (although this can be hand-waved)
That being said, it is not thematic or fun at all, and the writers knew it. So they released a splat a few years later that gave some rules for more magic-feeling casting, which still does not (by default) use spell slots or mana points.
And that's even ignoring how you can model stricter spellcasting systems as Advantages, with each spell being a specific advantage, effectively being a kind of superpower in practice
I would argue that FP more or less function as mana points in the default/GURPS Magic system.
Also, what splat are you referring to in the second paragraph, Thaumatology? RPM?
Thaumatology. And nothing says you have to spend FP to cast spells. It is suggested as a possible default way of doing things, and GMs will often make you do that, but it's not a hard rule.