I asked this question of a vendor several years ago and kept his responce in my email program.
"One pumps and the other one lifts.
They are typically interchangeable. But in my humble opinion, a lift station would refer to a sewage station, and a pump station would refer to a water booster station. However, I have referred to lift station as pump
stations, but never a pump station as a lift station.
Know what I mean."