How did this stone become encased within different rock? My father, in his younger years, was a stone mason in Cincinnati Ohio. A couple of decades ago he was building a wall of some kind. He would fetch rock from a creek bed, haul it to the construction site, then shape it with what he calls a brick hammer.
After giving one rock a good whack, he found that it contained a smooth gray stone about the size of a child's fist. One side of the stone is a little darker than the other. When cracked open the stone appears fairly homogeneous.
How did this stone find its way inside the larger rock?
EDIT: Removed my speculation (cited by one answer) and other clutter. Added example of stone used for the wall.



(click to enlarge)
it was simply an older stone smoothed by water that had fallen into sediment.

This is exactly what happened. There's a name for that: a conglomerate.