Background on Genes and Peaches
To expand a bit on this for the more advanced reader.....The seed inside the pit resulted from pollen from either the same or another peach tree fertilizing the flower that eventually became the fruit you ate. In this process the chromosomes in the seed are some combination of the female & male contributions. So, the peach tree that grows from the seed will produce fruit that does not closely resemble the wonderful peach you got the seed from.
Some of the more interesting pits to plant are from white peaches and from nectarines.
White peaches have a dominant gene for white color, meaning that the peach will be white fleshed even though the other gene (peaches have two of each chromosome type) may be of the yellow type. Sometimes the plants that sprout from a white peach seed is completely albino (white), with no chlorophyll (the source of the green color ). The plant often grows until the food in the seed is gone, then it dies.
Nectarine fruit are fuzzless because the tree they came from have only the nectarine genes. A peach tree has either one or two genes for fuzziness--the fruit will be fuzzy in either case because the gene for fuzziness is dominant over non-fuzziness.
So what happens when you plant pits from nectarines? If the pollen that caused the fruit to form was from a nectarine tree, the fruit has to be a nectarine.
If a nectarine tree is pollinated with pollen from a peach tree we have to know information about the peach tree variety in order to predict what will grow from the peach pits. If the pollen parent had only two genes for fuzziness, the plants growing from the new pits will be peaches. If the pollen parent had one gene for fuzziness and one for non-fuzziness, then approximately 50% of the plants growing from the new pits will be nectarines and 50% will be peaches.
The best way to get a tree that produces the same type of fruit is to find out what variety it was and then track down a nursery that sells trees of that variety.
Even if you can't find out what variety it was, you still can find several varieties of the same type that may be as good or even better. The growers and researchers with the Michigan Peach Sponsors may be able to help you with this quest.