Simply analyze the positional difference and similarity between Dragon and KID
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I am a player who play dragon and KID. Generally speaking, the biggest difference between these two is the pawn center. In main line of KID the center is blocked so that the black can launch a kingside attack. However in dragon the center is full of dynamic. Also in KID the c-file is closed and white tries c4-c5. In dragon c-file is a semi-open file which black would like to make a sacrifice with rook on this file. The similarity is the g7 bishop which controls the potentially most active diagonal. I really love both of them. Let's discuss these openings!
What's there to discuss? Those openings have almost nothing in common. As you noted, the fianchetto is the only real similarity.
I think that there are aspects in common between the two. The Yugoslav Attack against the Dragon and the Saemisch against the KID are conceptualised along very similar lines with almost identical deployments. There are other systems for white which are also similar for the KID and the Dragon (e.g. the classical systems that place the bishops on e2 and e3). Of course there are differences with the absence of the white d-pawn, the black c-pawn and the fact that the white c-pawn has stayed at home in the Dragon but not in the KID which shouldn't be minimized, but there are however also similarities, I would argue, that come out of white choosing more or less similar strategies to deal with deployments that similarly feature the black kingside fianchetto and a pawn on d6.