The grey water in an RV is water that is waste water that comes from the kitchen sink, bathroom sink, shower etc.
That water is dirty but not as dirty as the black water which is the sewage water.
RV's usually have two wastewater tanks and one is for grey water waste and the other is connected to the RV toilet which is for the solids or black water.
Grey water can sometimes be dumped directly on the ground or used to water a garden while black water which is sewage needs to be dumped into a RV waste dump for sanitary reasons.