emperor vs king.

An empire, roughly speaking, is stitching together a bunch of different places under one ruler, while a kingdom generally is one united land. The Roman empire, for instance, included a bunch of different lands which were conquered and conceptually still considered distinct although ruled together. Compare to, for instance, Sweden which is a Kingdom. But then the complexity is, the Kingdom gets some additional lands somewhere else, and then there's the Swedish Empire for a while. Then they lose those extra lands and you're back do the King having just his Kingdom.

It's a matter of perspective and can be a subtle distinction sometimes, but there is a conceptual difference there. An empire is not necessarily larger, but it will tend to be as it's a type of union essentially.