Emanator has two definitions: a person who enforces their Aeon’s will (their Path), and a person who can “draw directly” from the Path itself.
Arbiter Generals are confirmed to fit the first definition (enforcers of an Aeon’s will), but it’s still not confirmed whether they fit the second definition (those who draw directly from the Path).
Not to mention, HoYo really AVOIDS calling Arbiter Generals Emanators, which I think is VERY sus.
So, I think Arbiter Generals are people who simply wield an Emanator’s power, like Stoneheart or the Trailblazer. However, unlike them, their spirit is considered part of their body—not just a weapon by pistol rating—so that gives them an immeasurable rating similar to Emanators.