I have been told that if I were to plant the apple seeds from one of the trees in my yard, it wouldn't be the same, genetically, as the apples on the parent tree. Okay, I think I understand this, but here are a couple of questions:

I have two Damsom Plums planted next to each other. I don't believe that there are any other plums planted in the proximity, but there are some other "prunus" trees -a sour cherry, a sweet cherry and maybe another one or two other "prunus" that I don't know about (we live next to quite a bit of vacant acreage; I don't know exactly what is growing there.) Since the Damsons are right next to each other, wouldn't it be highly likely that the fruit, if planted, would yield an identical tree and fruit as the parent because of the high probability that the pollination was between those two trees? Therefore, progeny same as parent?

This brings up another question, as well: For trees that self-polinize, such as the Damson, wouldn't these ALWAYS yield identical trees/fruit when a pit is planted?

I'm sorry if my question is confusing. I could try to reword if need be. Thanks in adv. for any help anyone here can give.