There are no real standards in common names, particularly in the aquarium trade. There has been an attempt to standardise names within Australia, which are as follows (only based on the species I mentioned):
Cairnsichthys rhomboides - Cairns Rainbowfish
Melanotaenia duboulayi - Crimsonspotted Rainbowfish
M. fluviatilis - Murray River Rainbowfish.
M. maccullochi - McCulloch's Rainbowfish
M. splendida inornata - Chequered Rainbowfish
M. splendida splendida - East Queensland Rainbowfish
Pseudomugil gertrudae - Spotted Blue Eye
P. signifer - Pacific Blue Eye
Rhadinocentrus ornatus - Ornate Rainbowfish
Rainbowfish keepers in Australia usually keep fish from known localites, for instance you might buy a fish as "Melanotaenia trifasciata, Goyder River", rather than simply under the common name Banded Rainbowfish. Many of these forms have distinctive colorations and requirements, and not too surprisingly recent research suggests that many (if not most) actually represent distinct species. Unfortunately, many of the "Australian Rainbows" available in you aquarium stores in the US are hybrids, usually involving "forms" of M. splendida. Many of these are rather washed out in comparison with pure stock. If you are interested in getting pure stock (known species from known localities), you can get eggs or fish from people on some of the dedicated rainbowfish forum sites. There are some very helpful people on this site:
Rainbowfish Forum :: Index. There is also a society dedicated to Australian and New Guinea fishes (ANGFA - Australia New Guinea Fishes Association - see
ANGFA Home Page), which has branches in North America.
Tony