So, tell me…are these different types of apples sprung from different tree species or is there something else causing the variation?
The different varieties of apple are no more different species than you or I are. They’re just different individuals within the species.
Apples reproduce through bee-assisted cross-pollination: pollen from two trees is required to fertilize the stamen. Therefore, each seed produced is a cross between the traits of two different trees, and each seed has the potential to grow a unique individual. Plant the seed, wait for it to grow; three years later, you could find yourself as the sole progenitor of an exciting new apple variety.
Or, more likely, you’ll find that you’ve got a crab apple tree. There’s no way to tell what you’ll get until the fruits appear.
If you do happen to hit the lottery and grow a varietal worth reproduction, it’ll take some old-school cloning to make it happen. Grafting is the process by which, in the spring, when growth is happening at an exponential rate, a branch from one fruit tree is cored from its trunk and transferred to a correspondingly shaped hole in the trunk/ rootstock of a tree from the same species. When the grafted branch takes successfully to its new home, it will continue to grow apples of its own variety. Thus, it is entirely possible (and used to be common) to have a single apple tree yield 2 or more varieties of apple, depending on how many types have been grafted onto its trunk.
For more great information on the biology of apple reproduction, and the history of apples grown from seed (including information about how John Chapman [aka Johnny Appleseed], who got his seeds from the cider mills of Pittsburgh, was in the business of providing settlers with the means to make booze for the long frontier winter), check out Michael Pollan’s pop-ag classic The Botany of Desire.