What is the justification or definition that separates the two? I can't find any source (although I didn't try very hard) that states that Egypt was the world's first empire. I'm a teacher, and I want to be able to explain this to my students without contradicting myself or sounding like an idiot.
A clarifying question... The Egyptian empire was founded in ~1550 and the Akkadian empire was founded around ~2334. Where are you getting your numbers?
What I have typically read is that the general distinction between a kingdom and an empire is that an empire encompasses more than one ethnic group. The Egyptian kingdom consisted only of Egypt, whereas Sargon, who spoke a Semitic language, conquered Sumer, which did not.
This definition is supported by this paper in the first paragraph, and points to the original source of the claim of Sargon being the first emperor.
It wasn't until several hundred years later that Egypt conquered parts of Kush and Syria to satisfy this definition of Empire.