What is a wet well? A dry well? 

A wet well is the area at the pumping station where wastewater collects to allow pumping.  It is literally a well of wastewater.

A dry well is where the pumps and other equipment is located.

What is a pumping station? 

When low areas of land must be sewered, or when pipe depths under the ground surface become excessive, pump stations are normally installed. These pumping stations serve to lift the wastewater to a higher point to allow the resumption of gravity flow, or the wastewater may be pumped under pressure directly to a wastewater treatment facility.