Fate is one of the three axes of magic (along with Erf and Numbers) used to break a major class of magic into three different disciplines. Erf-b1-p038a Some Erfworlders also use the term "Fate" to refer to the predetermined destiny of an individual or group, as if it was a magical Stat.
Fate views or changes the purpose or destiny of whatever it deals with. For items, that is what it does. Turnamancy can take an existing object and make it work itself (adding Motion), but to take something and give it a purpose beyond what it has innately takes Dollamancy. When one form of regular Stuff is changed into another by a Changeamancer, it’s Matter and Fate. Healomancers directly modify the Fate of whatever they cast on. Fate Magic is more subtle than Erf magic, but less so than Numbers. Erf Magic has an effect that is immediate. Fate Magic tends to be more long-lasting. Changing the nature, purpose or direction of an object is a profound thing and that’s what Fate does.
The Axis of Fate seems to focus on an active target's status. For instance, Croakamancy can return a character from croaked to uncroaked. Dollamancy (and by proxy fabrication) specializes in the creation or re-configuration of a base material into non-living items like raiment, golems and small, non-magical items. Presumably, Healomancy restores hit points and removes other status effects. And Thinkamancy has been shown to alter loyalty scores. Predictamancy can determine a target's future state - alive, dead, carrying around an Arkentool.
Loyalty may be considered a form of natural Fate magic, in that being loyal to a side is aligning ones fate with it. This is probably, as Loyalty and Duty are described as natural Thinkamancy.