Part of the former Kingdom of Axum is included in present-day Ethiopia, but if memory serves correctly it didn't cover the entire area now included in the modern nation.
Axum is just a city (in Ethiopia) but the Axumite Empire covered a pretty big area and lasted a very long time. Neither it nor the ancient kingdom of Abyssinia have borders exactly the same as modern-day Ethiopia, though.
I'm pretty sure Abyssinia is what Ethiopia was called during Italy's invasion of it in 1935. It was pretty much exactly what constitutes the Ethiopian nation today, it had to be.
This is because Italy already controlled modern day Eritrea, modern day Somalia was jointly controlled by the UK and Italy, Kenya and Sudan were controlled by the UK, and even Djibouti was controlled by the French. Not much room left for border mutations.
Abbysinia is the same country as Ethiopia, just renamed. Axum is an acient empire that just happened to be partially in the same territory, without any real connection between the two. Kudos for knowing it, but would you say that Golden Horde is the former name of Russia? Probably not.
This is because Italy already controlled modern day Eritrea, modern day Somalia was jointly controlled by the UK and Italy, Kenya and Sudan were controlled by the UK, and even Djibouti was controlled by the French. Not much room left for border mutations.
I don't see anything in the quiz title or description that says it's a geography quiz.