Ethiopia is the rearranged Greek word "Aethiopia" meaning burnt face and referred to the Nubians in present day Northern Sudan. Habeshas stole the name less than 150 years ago.
Abyssinia only encompassed the Northern Ethiopian regions, so to say that the Adal Sultanate was fighting Ethiopia would be wrong because 1. Ethiopia didn't exist (or it didn't refer to the half Arab mutt rape babies known as Habeshas), and 2. Adal was geographically located in Ethiopia too, so were they fighting themselves?
The name Ethiopia has many sources including Hebrew...either way we have been self known as Ethiopia since at least the 3-10th century, and has appeared in numerous of books such as the book of aksum. When the Spanish did a reconquista of Spain from the moors, both polities were still inside the country of Spain. One was just obviously not apart of the original polity.