The snes one is kind of a sequel, as the same three characters appear. What changes is the Fire Hero, and in DKM2 you see where that hero comes from.
DKM is one of my favourite snes rpgs, it ticks everything I like in the genre. I still haven't played the famicom one, though, I have to do it one of these days (I fear it might be a little hard to play by today standards: lots of random encounters, excessive grinding, etc).
There's also Juvei Quest on the famicom, which is made by the same developers and it's one of my favorites on the system (it has lots of gimmicks that were implemented in DKM later, such as the helpers, etc). Let's say that, in Juvei Quest, the developers experimented with the features that were later ported to DKM and DKM2.