Have they always been here since the river was formed? Are some newer than others?
Riverbed 'stones' - I assume you mean things like pebbles, boulders, etc. are pieces of rock that have weathered out and been deposited in the river. Some come from rock that is very close to where they are located and some have been transported from very far away. In general (and it is a very broad generalization) the rounder the stone, the longer it has been in the river and the more likely it is to have come from far away. Of course that depends on the hardness of the rock, and other factors, too.
Some rocks are newer than others. Some have been formed quite recently and some are billions of years old.