BakerAunt, I grew up on an orchard in the north. Our peaches seldom survived the late frosts. During the few, glorious summers we had peaches, my sister and I would eat most of them straight from the trees, taking home only enough for Mom to slice and serve for dinner. We only had a few trees, because parents knew it was an iffy crop because of the weather. Some of our trees were freestone and some were clingstone.
As far as I know, the only way to tell the difference is to cut the peach open along the "crease." If the pit pulls easily out of the half, it's a freestone. Also, if it's a freestone, it's easy to pull the fruit into halves after cut. Clingstones make it difficult to cut the peach into halves, or to do so neatly. The pit clings to the peach.
I have no idea why the adults purchased clingstone trees. Even Mom had a hard time slicing them. The planting of peach trees was an experiment. Maybe including clingstones was part of the research.