In FF8 we're told that only Sorceresses and Monsters use true magic. Everyone else uses something called "Para-magic", in japanese it's "Giji Mahō". But the term is never elaborated on. A more accurate translation would be "Psudo-magic" or "False Magic".

There was a scene cut from the game, on the train to Deling City, where Rinoa would have asked what makes a Sorceress different from everyone else using magic?
At this point we would have learned about Dr.Odine for the first time. Everyone in the Galbadia Army uses an Odine device, not Guardian Forces. So para-magic may or may not actually be what Squall and the other use by stocking magic drawn from monsters and draw points.
Later, Rinoa shows up with an Dr.Odine Bangle to suppress the sorceress' magic. Zell vouches for the Dr.Odine "brand".

In FF13, the people of Cocoon (the moon) also have devices that imitate magic. Specifically, they're manipulating Antimatter (later called chaos) by copying and measuring how the Fal'cie do it naturally. AMP. Antimater Manipulation Principle.
You might call this "False Magic" too. Get it? 'Cause the Fal'cie are "False Gods". Where as the branded L'cie can do magic without the devices. We really only see this at the beginning of the game. Lightning does that anti-gravity thing a few times.

We learn much later in FF8 that monsters come from the moon. GFs have an unspoken connection to the moon as well with crescent icons, as well as the moon (as mentioned in the help menu) having the same ability to make people forget.

In FF16, most citizen's use crystals to cast magic. People who can cast magic without crystals are called bearers, but also, "branded" because they are tattooed and persecuted. However there are also "Dominants" that are essentially bearers but they can summon Eikons. Humans are actually part of a eugenic program.

Conceptually, all these ideas go back from before FF8. To Xenogears. Channeling aether is a genetic trait, making them tools of the gods