In her Masters of Rome series of historical novels, Colleen McCullough is careful to give all the terminology of civic and military ranks and offices (as well as priesthoods and foodstuffs and architectural terminology and a great deal else) exactly as the Romans would have used them, and each volume includes a helpful glossary at the back. She often uses the English word “general” to refer to an officer in command of a legion or group of legions – but no Latin term is ever mentioned, except for imperator (“commander”), which clearly is not the title of any and every Roman general, but only of those who had been “hailed as imperator in the field” by their troops following an impressive victory. I tried translating “general” through this online Latin-English dictionary and got three results: imperator, dux ducis, and communis. I know just enough Latin to know that dux ducis means “leader of leaders” – doesn’t sound like something Romans would have used as a military rank, at least in the Republican period – and communis almost certainly means “general” in a non-military sense, i.e., “the general welfare.” There’s also the word legatus, but I’m not sure if it translates “general” exactly; McCullough never uses it, at any rate.
I guess there are two questions here:
What formal rank title did the Romans accord the commander of a Roman legion or legion group? Was there any such word at all, or would a Roman general always go by some more specific title, e.g., that of his civic office bearing imperium (consul, praetor, proconsul, propraetor, etc.)?
What word (might be the same word, might be different) did they use to refer to a “general” in general, i.e., a word that might be applied to any force commander, Roman or foreign?
In Imperial times, at least, a legion would be commanded by a legatus, specificially, a legatus legionis, and under him, tribuni. Commanding more than one legion would be the dux.
More generally, dux could be used to refer to any general, in the Roman army or outside it. It just means “someone who leads”.
I don’t know the answer to (1); it’s been far too long since I read Roman history. But for (2), I can offer two standard usages, neither necessarily meaning ‘general’ in the sense of ‘person outranking a colonel’ but both conveying the meaning of ‘supreme commander of an armed force.’ They are magister militum, “master of soldiers”, and dux bellorum, “leader of wars/battles.” So far as I can tell, and this is WA Inference, the former seems to refer to a person designated as in permanent charge of a given military force, while the latter is the person who might head up a combined force, as of several units brought together for a given campaign or the commander by consensus of a group of troops and allies. But I won’t swear to the accuracy of that; it seems to be the connotation fir each of the two terms.
I think it kind of depends on where you draw the line.
If you look at a legion as roughly equivalent to a modern-day regiment(roughly size of a legion), then a Dux is generally the lowest rank that would correspond to a general, while if you look at a legion as being more like a division, then the Legatus is the lowest rank corresponding to general.
The Comes rei militarum were generally General officer-level positions, much like Dux positions were.
(FWIW, Dux and Comes devolved into the noble titles “Duke” and “Count”)
Field commanders for military operations were generally either subject to the proconsul of the province or the Senate (if in a senatorial province; also note that commonly the proconsul and commander of the legions in the province were one and the same). Hence legatus–quite literally from lego - “select”–was used to describe an envoy, legate, or lieutenant even when in command of an army because it was a subordinate position. This, I think, is as close to a formal rank of “general” as the Romans had.
Regarding leaders in general, Caesar refers to each of the various tribal leaders he faces as dux. The title imperator was a complimentary epithet–not a specific rank–applied to a leader after winning any significant battle, and so could be awarded multiple times.