The "wet well" is the structure that holds the water (potable or wastewater or stormwater). A "dry well" is generally an underground structure adjacent to the wet well where the mechanical equipment is housed (i.e. the pumps, valves, maybe the MCCs and switchgear). Generally the dry well is at the same elevation as the wet well, or close to it. That's the most basic definition.
That said, there are many variations. Submersible pumps can be installed in the wet well, so a dry well isn't needed. Or, perhaps the pumps draw water directly from a river or sewer, in which case there is a dry well but no wet well. The benefit of dry wells is a convenient place to perform maintenance on the equipment...the downside is additional cost and an unfortunate possibility that it might flood (which is why placing the electrical equipment below grade is not advisable).
