Interesting thought on temperature, not suprising really if you think about what a wide area we get corals from.
I'd call these pieces maricultured, IMO Aquacultured means it's something that was grown in aquaria = second generation.
[IMO, new growth in the aquaria cut to a new colony = aquaculture, cutting up a wild coral into pieces and letting it encrust isn't - and this is similar, though the ocean context is different than having proven to live in aquaria for a while].
People vary on what they classify what, but that's the line I draw. Personally, I prefer the coral having been in at least two prior aquaria/keepers - as there's a sense then IMO that it deals well with the fluctuations and nutrient issues that it will experience in aquaria - and I've rarely had problems with a coral that's a frag of a frag, all from aquaria. That said, if I'm looking for a coral from the ocean, I've recently gone with mariculture/ocean aquacultured pieces vs. wild or wild aquaria-encrusted frags [like a number of places offer].
But the ocean aquaculture/mariculture are often very lovely corals, some really stunning varieties - and hopefully/likely of less impact on the reef. Seems like sometimes very unusual pieces, sometimes fairly similar pieces. Just wish there was some sort of guide to the bases, so we could ID which producer our stuff is coming from.