"Türkiye" isn't Turkish. It originates from Latin "Turchia" (land of Turks) and later French "Turquie." Actually, "Turkey" is anglicized form of "Turquie." So, there's no difference between two words apart from that both got adapted to the phonetic repository of their respective languages. So, even if all English-speakers start using "Türkiye" today, it'll probably degrade to "Turkey" anyway. This was such a waste of resources.

"Türkiye" has no meaning in Turkish. Proper "land of Turks" in Turkish would be "Türkyurdu" ("yurt" meaning home/homeland, yes, the same word for those large tents as they were the homes of nomadic Turks in Central Asia).