No. it means same. But it was created different era of turkic language / mongol language that gets extra meaning. it all originated from ḳaġan/χaġan/χān.. Similar likeKaan means khagan, not khan. Khagan means khan of khans.
Khan(Han)= King level ruler
Khagan (Kaan, Hakan, Kağan)= Khan of Khans emperor level ruler.
Timur/tegi / temir/ demir/ teymour/ etc etc.