The Romans had no precise word that corresponded with "general." The right to command troops, and to inflict corporal and even capital punishment in order to effect that authority, was termed imperium, and the term for the holder of imperium, an imperator might be the closest counterpart of English "General." Only two elected offices came with imperium: the praetorship and the consulship. The imperium of the praetor was consider inferior (minus) to that of the consul. While the term of these offices was only for a single year, the imperium might be extended beyond to allow the holder to continue in a command; the decision was usually made by the senate, although sometimes through a popular vote. These were therefore pro-consuls and pro-praetors.

Finally, in rare cases, someone could be granted imperium by a popular vote even though they had not been elected to a magisterial office. Thus in 210 BC, Scipio Africanus was elected to a proconsular command in Spain, despite never having held office as a praetor or consul. For this command, he was an imperator sine magistratu--an imperator without an office.

So the imperators could be consuls, praetors, proconsuls, propraetors or imperatores sine magistratu. By merit of holding imperium, they had the legal authority to command troops (this came with the closely related religious authority, auspicium, the ability to take public auspices to determined the will of the gods).

Now, imperatores often needed subordinate officers. In addition to military tribunes, elected by the Roman people, imperatores often appointed trusted friends as legati, "picked men," although here we could call them lieutenants in the high sense of the word (i.e. NOT LTs), someone to whom the imperator delegated command functions. They also served as hand picked advisors on his military council. An imperator could delegate a legate to command a legion in battle, or to oversee a detachment or detail. Unlike military tribunes, usually younger men at the start of their careers, legates were usually peers of the imperator, indeed often former consuls were brought on as legates to provide their counsel and experience to the current consul's campaign.

Things get complicated as we transition towards the empire. Pompey the Great in 55 BC was granted an extended proconsular command in Spain. But as he was also in charge of the grain supply in Rome, he was allowed to command in Spain remotely, sending legates to exercise delegated command while he stayed in Rome.

When Augustus finally established the imperial monarchy, this is the method that he adopted to command his armies. Technically, Augustus was the commander of almost all the soldiers in the empire, by virtue of being appointed the governor of almost all the militarized provinces. In 23, he was even grated imperium proconsulare maius, "Greater Proconsular Imperium." His imperium was so stupendous, that he even took Imperator as his first name, and thus we the origin of "emperor" in the sense of "absolute monarch," instead of previously as "popularly elected general." But Augustus could not personally command 25-28 legions spread across the empire personally. Like Pompey, he stayed in or around Rome and dispatched handpicked legates to exercise delegated command. Provincial governors were legati Augusti pro praetore "Legates of Augustus, with propraetorian authority" (although note, they did not possess propraetorian imperium--they were delegates exercising Augustus' imperium). We often refer to these men as "generals", namely as men entrusted by the emperor to substantial military commands.

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Throughout I am heavily influenced by Frederik Vervaet, The High Command in the Roman Republic: The Principle of Imperium auspiciumque (Stuttgart 2014).