...and why do they often differ from what said country/culture calls itself? For example, a person we call "German" from "Germany" would call themselves "Deutsch" from "Deutschland".

And even stranger is our terminology for Eastern nations. Ex: "Japan" and "Japanese" vs "Nihon" and "Nihon no".

Obviously some of these terminologies make sense, especially countries where the primary language is latin based "Italia/Italiano" "Mexico/Mexicano".

But how, when, and why did these variant terms come into use?