I'm under the impression that empire is generally a collection of nations being administered collectively, generally under a single ruler called an emperor, rat

I'm under the impression that empire is generally a collection of nations being administered collectively, generally under a single ruler called an emperor, rather than just being a term for a powerful nation. The British Empire ruled the UK and numerous colonies and the Holy Roman Empire ruled over a collection of Germanic states. Except for a few exceptions (e.g. Guam and Puerto Rico) the US is all one nation and governmentally not an empire