Any of these could act as seed potatoes… and so can the potatoes that sprout in the cupboard if they are stored for too long.
This is the reason that I find occasional potato plants in odd places in the garden. Unless the patch is required for something else and the potato plant just can't remain, I leave the whole thing there and wait for it to go through the leafy phase and the flowering phase (though not all potato plants flower in my garden) and when it dies down, I dig up the tubers.
Whenever I think I have harvested every last potato, there are invariably a few remaining… and these become the seed potatoes for the misplaced crop of next year.
This is probably why my garden is not very neat and orderly, but it's also why there is always some food for dinner.