In your example, there is is no real distinction
I threw a rock
I threw a stone
and most people will not make an explicit distinction
Rocks in His Pockets
Stones In His Pockets
However, to geologists, a stone is made of rock, but a rock is not made of stone.
Rock is considered the material.
A stone is usually thought to be smallish and can be handled.
To possibly add some confusion to the naming scheme, there is Stone Mountain which certainly won't fit in your hand and is made of rock, and there is also Rock City which is a collection of rock formations.
Now, if you were to ask the difference between getting rocked or being stoned...