I would say related but not identical but I'd need to research it to be sure how to make the proper scientific argument. But my rationale is as follows. The pollen and ovum each have half of the genetics. For those genetics to recombine in each seed to create a clone, you'd have to argue that every pollen was identical and every ovum was identical so they recombine the same. But if that were the case, every cross for a pair dolgo and antonovka trees would also produce seeds that were an identical mix. Every seed in every apple would produce an identical tree. But apple sex doesn't work that way.
Instead, I think that each pollen and ovum from the same tree are different split of the original genetics. So each resulting self-cross is unique. So if a Dolgo has a gene pair of dominant red leaf and recessive green leaf, you'd expect the self-crossed seeds to 25% red/red, 25% red/green, 25% green/red, and 25% green/green. Then 75% of the seedlings would be red leafed and 25% green leafed (assuming that leaf color is all controlled by a single gene but I think it is actually more complex than that).
The exception is for trees that produce apomictic seeds, in which case all the genetics are a clone of the mother tree and the source of the pollen (self or cross) plays no role.
The third scenario is parthenocarpic where the flower was not fertilized by the pollen but produces fruit without seeds.
