Ok...the empire became an empire when we took over India from the Honourable Company. The empire consisted of all our colonies and dominions, including places like canada and australia, though these became increasingly independent. We ruled them from here, basically. The Commonwealth is voluntary and is largely made up of our ex colonies, and is simply a fraternal group...although many states still recognise the queen as head of state, and have a govewrnor general, they are self governing. In fact some countries we never subjugated have joined the commonwealth as a trading organisation..
Firefly...an emperor is a monarch. In terms of usage an emperor is probably defined as a senior king who rules over lesser kings. The first commonwealth was ruled over by parliament (then cromwell), the monarch having misplaced his head....