All I really know is that there is a difference between dwarves and pygmies. I think* that H. zosterae are dwarves and the others are pygmies (could be the other way around). But anyways, the differences between the two (dwarves and pygmies) such as the corals they need to survive, food requirements (extremely specific to each different type and where they occur), and size. Now let's also remember that since they need the certain corals or gorgs to survive, that means we would need to keep those corals or gorgs extremely healthy too. The whole concoction of problems is just well, --->:hmm4:... A bit too much.
That is correct, dwarves and pygmy seahorses are different. There is some speculation that the pygmy seahorses may even need to be grouped into their own genus. What we do know is that Bargibanti branched very early from the rest of the seahorses, where Hippocampus zosterae is more closely related to Hippocampus erectus and Hippocampus hippocampus.
I don't believe genetic studies have been done on the others yet to determine their relationship; but considering the morphological similarities to bargibanti vs the rest of the seahorses, chances are they too are from the same branching.
So even though dwarf seahorses and pygmy seahorses are superficially similar, they are very different animals that require different care. Also keep in mind that pygmy seahorses are smaller than dwarf seahorses. This adds a whole new dimension to providing the appropriate environment.
As for keeping pygmy seahorses by way of keeping their host corals? If only it were that easy. The Waikiki aquarium tried to keep Muricella coral and H. bargibanti, and despite their best efforts, the coral died, and along with it the pygmies. There is a lot work emerging regarding keeping non-photosynthetic corals in captivity, both in public aquariums and on a hobbyist level, but we're not there yet.
Another concern, quit frankly, is that they could easily become overfished if they were to be harvested. While very little is known about them, they seem to have an extremely small range. Their young are rather well developed, meaning they likely do not travel far, and they only have a few at a time. That means any collecting beyond a few individuals may decimate the population to the point of no return. Much like what bangaii cardinals are facing right now; of course the difference is this could end up being far worse since their habitat is SO localized.
The good news about that though is the locals are very protective of their pygmy seahorses. They fuel a lot of dive tourism, and often won't share where their known seahorse holds are. I suspect that would lead to them being very defensive about anyone trying to remove their seahorses. And my understanding is that they're very hard to find on your own, most divers go to a guide that knows of just the right spot to find them. So even if you had the proper paperwork, chances of you actually finding them is vanishingly small.
Incidentally, not all of the pygmies seem to be reliant on a host coral. A few live no-specifically on algae. If any were going to end up being suitable for captivity, it would likely be these. However there is still too much to learn about them before it could be determined if its even possible; nevermind the potential ecological harm I mentioned above. It's a pretty sure thing that any "copepod rich" thank would not stay that way with any seahorse species; it's been tried with copepod feeding animals and they deplete the tank population extremely quickly. And growing copepods in large quantities - if that turns out to be the right foodstuff, is labor intensive. Even if you can overcome those hurdles, its still not clear what else they might need; and I for one don't want to see them brought into captivity only to perish while we "learn more".