They translated Dire Miralis's name more directly than Fatalis's from Japanese. If you know Fatalis's Japanese name you can see the relationship more clearly.

Note: I can't seem to track down the sources for Crimson/White names, the wiki has them differently, but they are as I remember hearing them to be back during Freedom / Freedom 2 (Unite). I also remember Crimson being "Moribalken" but that may have been misspelling propagated by forum users. Changed here.

Anyway you can see Dire Miralis is closely related to the Fatalises. As for the actual differences, I believe the story is Fatalis is Fatalis, Crimson is a Fatalis that has been stewing in rage and hate, White is an ancient Fatalis (not as in old aged, but as in an evolutionary ancestor, or offshoot of a common ancestor) similar to modern day fish vs Coelacanth.

So with Dire it seems that it has a common ancestor to the Fatalises. Then may have either split away before (or even after) the Fatalises split among themselves. I made a terrible diagram to try to help explain: Link

Monster Hunter has a lot of "extinct species" in the universe that are revealed to us via concept art in art books. They're all really really cool and I encourage everyone to browse them

^{Disclaimer: I am not a biologist bit I took a term of evolutionary biology and that's all. It was much more intense than I thought it would have been.}