you may call your wasted water "wastewater" and you may treat your "sewage" in a "water" treatment facility, but that terminology is completely twisted around for this region of the sphere...
here - all fluid (and solids) going to the POTW (aka stp, wwtp etc.) are called waste water. Often, there is pre-treatment of industrial wastewater, before accepting into the publicly owned sewer system. This is determined by the owner of the sewer system and is a permit requirement for connection to the system. Generally the treatment facility is a "wastewater" treatment facility. And for convenience, all lines are called sewers. Even the storm drains are often called storm sewers, therefore implying that they carry sewage. Alternatively, a "water treatment" facility is used for filtration and chlorination or other necessary treatment of river water for use as potable water.