I have planted an alomond tree about 5 years ago. On the forth year it produced sweet almonds. I enjoyed eating them at their peak while still green (dip them in little salt). However, this past summer after the tree had bloomed and produced the almonds in May, it started producing medium size edible and sweet peaches in July-August without changing the leaf shape, size or color. How is this possible? Is it a random propagation? The tree gave me about 12 lbs. of lovely sweet peaches.
Grafted onto a peach. They are closely related, in fact a common "almond" tree called 'Hall's' is actually a cross between the two. Cut off the peach sprouts if you want to favor the almond tree.
I believe that budding (or grafting) peach onto almond (as a rootstock) is fairly common. Maybe the nursery mixed it up or didn't see that the peach scion/bud took, and just sold it as an almond. You ought to be able to see the graft union if you follow the branch that bore peaches down to the trunk. If there are no grafts and the tree is producing both kinds of fruit on the same branches, well, that is unheard-of.