An AuthorityFile is a listing of synonymous terms that singles out one of the synonyms as a canonical or preferred term.
For example, if you want to tell your software "when someone searches for 'Elizabeth Fortensky', instead do a search for Elizabeth Taylor", then you are essentially saying two things:
A data structure that says this sort of thing is called an AuthorityFile. If you only said #1, without specifying which synonym is canonical, then it would be a SynonymRing.
If you have a set of synonyms and one synonym has been singled out as the "preferred term", then the other synonyms are called variant terms.
See also SynonymRing (which is like an AuthorityFile without choosing preferred terms).
See also Taxonomy (which is like an Authority file which also specifies a hierarchy of broader and narrower terms).