You are saying Khan and Khagan are the same thing they are related but not the same. Especially not in the context of Turkish usage. Even during the Ottoman times Crimean "Khans" were vassals of Ottoman "Kağan/Hakan". In Turkish use, khagan means khan of khans and is a higher title than a khan.
Etymological POV it is the same
as for context of using Turkish. You use "ne haber" in many ways too, to ask many things 10+ ways
. You see Turkics as nomadic nature are very simplistic the word "Deniz:sea" which comes from tengiz/tenggis also means ocean. Old baikal lake was considered tenggis (ocean) as immerse size. which is why the
Genghis khan name /cengiz comes from (Tenggis: deniz ) its same word. But uses as metaphoric way of Ocean immerse size as : huge/Universal.
That what's all about. As for Turkic language history khan, han, kagan ,kaan came from different era or different Turkic/mongol language adaptation . Similar as. it's you can find "Turkmen" 4+ meaning in the context of Turkish usage also in historical timeline. While all comes to same word.