Look, you're approaching this with WAY too much formality.
You're lucky if the manufacturer even knows what the board does, or how it works. Frankly they put some parts on a board, and it seems to sell. Whether there's design intent behind that (or just copycat, or a wholly random walk at all), let alone any kind of support or service infrastructure -- irrelevant. It's just a board from Ali (or Amazon, or eBay, or..). It's nothing more and nothing less than the circuit you see in front of you.
If I had to guess, assuming that the circuits are the traditional kind, for the traditional meaning of what that is (which, realize, is quite a stretch given the vast space of possible circuits that might be described using these few vague terms -- but given their popularity, this interpretation is still most likely to be correct); I would guess that the three-terminal one -- because it has one inductor rather than two -- is made for centertapped windings ONLY, while the other one can use either arrangement (just leave the CT unconnected).
If it means you got (or are about to get) scammed because you bought something you have no idea how to use, or that means you can figure out some use (maybe not the original desired or intended function, even), whatever -- so it is.
Tim