The Imperial Period, the Pax Romana, and the reign of Augustus are all different things even though they overlap to some degree.
The term "Imperial Period" refers to the time when Rome was an empire ruled by an emperor. It is typically seen as going from 27 BC to 476 AD. Before that, Rome had been a republic. So you will hear references to republican Rome as opposed to imperial Rome.
The Pax Romana is a time when the Roman Empire kept (or imposed) peace in most of Western Europe. It lasts for a long time -- about 27 BC to 180 AD. This is all during the time of the Empire, but the Empire lasts longer than the Pax Romana.
The age of Augustus refers only to the time when he was the Emperor. This, of course, was not as long as the Pax Romana or the Imperial Period. He reigned from 27 BC to 19 AD.