Counter would be a long continuous shelf along the wall. A workstation would be more clearly defined. You could stand or sit at a work station. A desk would be like a workstation, but definitely for sitting at.
You could rewrite your description:
There is a fixed work station against the wall where one can conveniently work. There is no chair located at the work station, so the users must stand to do their work.
*** Not a teacher ***
Student or Learner