Though it is true that a moderator is a rough equivalent of similar "governing" words like dux, curator, or arbiter, there is an important nuance that should be kept in mind when using it.
An important clue comes from its provenance: it is a verbal noun derived from moderor, -ari, which has a specific literal meaning:
I. Lit.: moderate, mitigate, restrain, allay, temper, qualify
This literal meaning obviously comes from modus, -i:
A measure which is not to be exceeded, a bound, limit, end, restriction
It is only in light of this literal meaning that the "governing" meaning came to be:
II. Transf.: to manage, regulate, rule, guide, govern, direct
My contention is that many uses (though certainly not all) carry the important nuance of limitation or restraint: if I am correct, a moderator militum is more concerned with making sure they do not step out of line, rather than leading them in a charge, as a dux or imperator might be. One good example where moderator is appropriate but other words are not is from Ovid, who is describing a horrible sickness and then remarks:
Non stratum, non ulla pati velamina possunt,
dura sed in terra ponunt praecordia; nec fit
corpus humo gelidum, sed humus de corpore fervet.
Nec moderator adest, inque ipsos saeva medentes
erumpit clades... (Ov Meta 7:558-562)
They cannot bear any coverlet or sheets,
but instead place their bodies on the hard earth; nor does their body
cool down in contact with the ground, but the ground heats up from their body.
Nor is there any one to provide relief, since the raging illness
has infected the healers themselves.
- There is no specific public or private function referred to by moderator.
A moderator is one who provides a modus to something.
a. This can be figurative, in which case its meaning isn't much different from other "governing" words, or:
b. This can be literal, in which case it specifically refers to restraint (moderator libidinis) or limitation.