Current is a chargue displacement. Current is charge in movement.
In that expression you can see charge distribution in channel, but those charges are in movement. That charge distribution defines a current path that is equivalent to a constan resistance. Then you have a constant current, you have a constan charge flux from D to S, but in each instant, chargue distribution inside the channel is not uniform. That means that not all thargues travel at the same speed, or that not al chargues are in movement.