Magic is probably innate, rather than drawing on outside forces. Of course then you might ask, "Well how do water and ice spells work then?" Might as well ask "How does ANY of it work then?" I mean, a guy generating a lightning bolt is just as far fetched as a Frog generated a giant wave. As much as we must disregard certain battle elements in their relation to the physics of the Chronoverse, the point about MP makes sense. Alternatively, it could be the energy one exudes in order to manipulate a specific element (CT, not CC) that lies outside of the person's being. But then that doesn't explain why Shadow users can use the other three Elements (even if you accept that Lightning+Fire+Water=Shadow, how does one use all of these if the Element of Shadow itself is not a fundamental part of you).
To keep in mind an important point, let us not forget Zeal. They all could use magic innately, though after the kingdom fell, magical ability began to be present only in the Mystics (according to the retranslation). Which suggests the need for a catalyst. The Zealians (zealots?) had the Frozen Flame, the Mammon Machine, and artifacts like the Sunstone. Crono's & Company had Spekkio (the God of War). Another fun thing to consider is Spekkio's specific statement that you needed a certain something in order to use magic. He said strength of heart in the NA translation, but I can't remember just what the Retranslation states. Anyway, he suggests its a specific potential you have on the inside.
I think the line should be drawn between Elements from CC and magic from CT. While the Elements are probably based at least somewhat on CT's four element system, its largely a separate thing. I believe that the mechanics are somewhat different if not entirely different. For instance, CC Elements seem to allow for that Energy grid to fill, allowing certain attacks to be stronger and others to be weaker. CT doesn't make any mention of such a thing so I assume its primarily a feature of the Elements.
More ramblings later.
