I'm not sure if either one is a good fit of analogy, given the way their nature seems to shift from wild to domesticated by virtue of nothing other than being caught. I've seen the occasional exception, creatures that don't take well to being under the control of a trainer and so they rebel as a result of it, but for the most part they seem to make the transition from wild to tamed in a surprisingly short amount of time, and with very little resistance to the idea of being controlled once they're caught.

That said, once they're in a trainer's care, they do seem to become domesticated — regardless of how that domestication sets in. And given that this is a world apparently designed to encourage people to catch and train these creatures to respond to human command, the dog analogy seems more apt than the alternative.