"Full marine" means that the salt levels will have to eventually be at (or at least very close to) the salt levels of the ocean. Generally an SG (specific gravity, a measure of the saltiness of the water) of 1.024-1.026 or so is considered full marine.
No, this does not mean you have to have corals and things like that. Your puffer is not reef safe, so corals and other reef inhabitants would likely just get eaten by your puffer. But it does eventually need to be in a marine, fish-only environment.
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