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The great debate: Spells Slots vs. Magic Points
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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.