As far as I have heard, “volunteer” potatoes would be something you want to stay away from.
A “volunteer” plant is one that grows from seed. This means cross breeding. Since there are so very many solanum species, potatoes might just latch onto something a little dangerous...
Potatoes that just grow from potatoes left behind in the ground from last year are fine. Heck, I haven’t bought potatoes in years, I just wait for the stragglers to sprout or actually plant potatoes I have bought (to eat) to sprout.
It is the latter sort of. We had so many potatoes last year, that I left a 16 sq ft. bed in the ground intending to dig it up in November after we had eaten some of the ones we dug from another area.
During cleanup, that bed got covered up with all manner of leaves, straw and plants pulled from the other beds at clean up which was never completed either. I had forgotten all about the potatoes.
When planning this year’s garden, I realized it, and uncovered the bed, and sure enough there were some leaves. Then a big frost, and some of the leaves turned black, but there was enough left that all are surviving.
Hubby had claimed in years past that we could just leave them in the ground till the next spring, and have potatoes get an early start, and I tried it one year, but guess they weren’t deep enough or covered enough cause it was a big failure.