What's the difference between emperor and king？

[True Federalist (진정한 연방 주의자)]

Emperor also typically implies that the sovereign’s realm includes colonies. For example, Queen Victoria was Queen of the United Kingdom of Great Britain and Ireland, as well as Empress of India.

Not necessarily colonies, but yes, typically a kingdom was generally considered to be one unified realm, while an empire was comprised of multiple realms. If it weren't for the desire to eliminate local parliaments, leading to the Acts of Union in 1707 and 1801, Victoria probably would have been styled Empress of the British Isles, Queen of England, Scotland, and Ireland, Defender of the Faith, even before adding Empress of India to her styles.

Also, in the pre-Napoleonic European tradition, besides an emperor outranking a mere king, a king had only secular authority, but an emperor also had some degree of religious authority, which is why before Napoleon the only European emperor was the Holy Roman Emperor.

[True Federalist (진정한 연방 주의자)]

Emperor also typically implies that the sovereign’s realm includes colonies. For example, Queen Victoria was Queen of the United Kingdom of Great Britain and Ireland, as well as Empress of India.

Not necessarily colonies, but yes, typically a kingdom was generally considered to be one unified realm, while an empire was comprised of multiple realms. If it weren't for the desire to eliminate local parliaments, leading to the Acts of Union in 1707 and 1801, Victoria probably would have been styled Empress of the British Isles, Queen of England, Scotland, and Ireland, Defender of the Faith, even before adding Empress of India to her styles.

Also, in the pre-Napoleonic European tradition, besides an emperor outranking a mere king, a king had only secular authority, but an emperor also had some degree of religious authority, which is why before Napoleon the only European emperor was the Holy Roman Emperor.

*the only Western European emperor. Obviously there were Orthodox emperors as well.

Those heretics clearly don't matter. Otherwise why would the infidel Mussulmans have been able to conquer Jerusalem and the Second Rome?   

[True Federalist (진정한 연방 주의자)]

History teacher here

King/Queen rules a unified homogeneous place. The people in the British isles are lumped together as one people. Queen Victoria was a empress because she ruled multiple places of multiple people

I think the Scots and Irish would disagree with that assessment.