Snakehead Taxonomy: Kingdom Animalia, Phylum Chordata, Subphylum Vertebrata, Superclass Osteichthyes, Class Actinopterygii, Subclass Neopterygii, Order Perciformes, Family Channidae, Genus Channa, Species Channa argus.
Bowfin Taxonomy: Kingdom Animalia, Phylum Chordata, Subphylum Vertebrata, Superclass Osteichthyes, Class Actinopterygii, Subclass Neopterygii, Order Amiiformes, Family Amiidae, Genus Amia, Species calva.
Not related as far as fish go. Comparison:
Order Perciformes: also called the Percomorphi or Acanthopteri, include about 40% of all fish and are the largest order of vertebrates. The name Perciformes means perch-like. They belong to the ray-finned fish and comprise over 7000 different species, with varying shapes and sizes, found in almost all aquatic environments. They first appeared and diversified in the late Cretaceous.
Order Amiiformes: The bowfins are a primitive ray-finned fish. Only one species, the bowfin Amia calva, family Amiidae, exists today, although additional species in six families are known from Jurassic and Cretaceous fossils.
So, the bowfin has a more primative lineage, first appearing millions of years earlier than the fishes of order perciformes. They did not give rise to the perciformes. The bowfin or dogfish is the only surviving member of this primitive family of fishes. Perciformes (perch like fishes) however, are very diverse.
So, in short, they ain't related
Still, they look similar, long rayed dorsal fin, big nasty toothed mouth. I think that the scales on the bowfin are large, and the snakehead has a more slimy appearance, maybe smaller scales.
Here's another pic (this one caught in Malaysia):
Here's a pic of the bowfin:
