The difference is shown graphically here:
Left is the intake tower (Wasserentnahmeturm = Water Collection Tower = Water Intake Tower) for regular withdrawal of water, right is the spillway tower with the conical inlet for overflow control (Hochwasserentlastungsturm = Floodwater Release Tower = Spillway Tower).
In fact both are tower constructions but the term “spillway tower” is unusual to my knowledge, commonly these are know as “bellmouth spillway”.