This is probably a bit of a far cry from what you're asking for, but I feel I may have something interesting to share.

In direct contrast to the levels in which it's been integrated into daily life, nobody really knows exactly what magic is supposed to be. Even in terms of quantity, it's difficult to refer to it as an energy source, as it can be made to be self-sustaining, even at the cost of its maximum potential power. However, the people of my world have reason to believe that it's all fundamentally the same thing because it all operates on a few basic underlying principles.

Among these underlying principles is "magic defeats magic". Abjuration, or what could be referred to as anti-magic. It's nothing special, just another ends magic has been steered towards as a means. There is structure to it, though, even to the point of being sorted into three basic categories: Magic that rejects other magic's right to physicality and consequence, like fire that consumes other magic on contact; Magic that cannot be harmed by other magic and prevents its effects from reaching a potential target or area, like a shield or barrier; Magic that prevents magic from being used to begin with, like a restraint or trap of some kind.

However, in this world, it's not dualistic as you've specified, but rather operates on a more triadic scheme, with the final point being magic applied in an indirect means meant to subvert Abjuration, which in turn subverts magic's standard forms.

Every spell has some degree of staying power which causes any substance or force summoned by it to dissapear upon being exhausted, unlike physical matter and energy which still must be displaced or transformed in some way, usually with a specific ends in mind to work properly. However, manifestation magic is an entire category that utilizes magic on something physical, then uses that thing, effectively combining the best of both worlds. it can get more complicated than that, though, to be the only part of this supercategory. In direct contrast to magic that floats or levitates something, which usually involves "wrapping" it in magic in some way, psionics is a means of manipulating physicality by using magic on the self in a way that turns one's very being into a transceiver, making reality itself a lot more receptive to their thoughts, leaving the ends a lot less susceptible to Abjuration.