An empire or kingdom or duchy are more than just names, they are actual defined terms, though the actual definition differs from region to region.

Generally, a duchy, ruled by a duke or duchess, would be a segment of a greater kingdom, and the duke/duchess would be, to various extents, under the authority of the reigning monarch, though there have been independent duchies in the past (these would have been too small to be considered kingdoms on their own, or the reigning duke simply did not or could not exercise the level of authority that a kind could).

An empire, generally speaking, is something like a kingdom that extends its direct influence to other states, usually from military conquest or colonial expansion. Examples are the British Empire who had overseas colonies as well as directly controlling India, Napoleon's French Empire that was expanding militarily, and the Japanese empire that took over Korea and further expanded into Asia during World War 2.