IMO these are suckers. Yes, left to mature, probably plums will one day be produced. However they will be different from your valued plum tree. Most trees etc are now produced by grafting onto a different rootstock. The graft can be recognised by the lumpy part of the trunk close to soil level. Any growth from below the graft, will more than likely be suckers. Suckers can be seperated and grown on seperately, but they will be offspring of the original parent.
Thank you for your reply
So how do I separate them, just pull them up? Put them in a pot with rooting compound?
But really, I don't know if I want to be bothered with plumb trees anymore; they have a very little usable yield (mine anyway). But you never know.