It seems from everything I've read on the Empire, the consistent term for the Emperor was Augustus, and Imperator was a much more vague title that was also bestowed on Generals who were not connected to the monarchy in any way. But Imperator became the term for an Emperor, and Augustus doesn't seem to have any continued use. Why and how is that the case?
The title 'Imperator' in the Roman Republic means 'person with authority to command' and would mainly have been held by consuls and proconsuls (until the late republic when warlords such as Caesar, Pompey and Sulla held the titles permanently). However by the time of the empire it was held exclusively by the emperor, apart from on a few occasions when it was given to a close family member (usually an heir).
The title 'Augustus' meant 'honoured one' or 'revered one' and was a somewhat obscure religious term prior to being adopted by Augustus.
While today we typically refer to Roman Emperors as 'Augustus', in reality they had much longer titles that generally included any number of honourifics, but almost always 'Imperator' and 'Augustus'. For example, Octavian's full imperial title was 'Imperator Caesar Divi Filius Augustus' (commander, Caesar, dutiful son and revered one).
I presume the reason we typically refer to Roman Emperors as Augustus and not Imperator is to distinguish them from commanders who held the title previously (particularly Caesar, who was never emperor).
As for why Imperator made it into modern terminology, I cannot say for sure but I strongly suspect that it relates to the Holy Roman Empire. The official title of the Holy Roman empire that was bestowed by the Pope was 'Sacrum Imperium Romanum', and the title of the emperor was 'Romanorum Imperator Augustus', however was more commonly shortened to just 'Romanorum Imperator'
If anyone has a more likely explanation I'd love to hear it!