Core has nothing to do with what is allowed in a game, though in
3e it was a shorthand references to no splat books. Core means that when
WotC releases a book with additional powers in it, you can expect that they assumed that you not only own the PH1 but also might own the FRPG. So arcane power has stuff that helps the swordmage. Similarly, the next arcane power book will have stuff that adds to the artificer.
For
3e, if a class was released in a splat, the only place you'd find stuff that helped it would be in that book. New spells/feats/PrCs would often not even be aware that the class existed, but instead only added to the core 3 books. When
WotC says that everything is core, they just mean that they continue to bring out additional material for stuff not in the ph1 or dmg1.
What this has to do with the allowed books for a campaign, I have no idea, other than removing the shorthand of what is allowed.
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