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.
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.