Perhaps there are more kinds of "other potato" than you are aware of. Some varieties of potatoes are poisonous due to naturally high alkaloid levels in the tubers, even without being exposed to light. In particular, one reason that native (south) Americans devised the freeze drying process to make chuno was that native potatoes had high levels of alkaloids and needed that processing to make them safe to eat, just like cassava has to be processed to be made safe. Nowadays they have selected potatoes for low alkaloid levels, and making chuno is done for preservation and because they (strangely) like the taste.

So if you grew potatoes from seeds, ones that set in the fruits (I don't know how easy that is to achieve) rather than "seed" tubers, one might be concerned they would not breed true but revert to a wild type, and have high alkaloids. After all people don't propagate from seed, which is usually cheapest, so probably there is a good reason why they don't. But in general, I have not heard of volunteer germination of potato (true) seeds taking place.

But since it seems these are volunteers from forgotten underground tubers, not fallen seed, then they are vegetatively reproduced, and the same as the
ones previously collected.