Control and operation are key differences between the outflow valve, over-press, and negative pressure valves.
The outflow valve(s) is/are under the command of one of two independent pressurization controllers under automatic operation, with position selection by the flight deck crew during manual ops.
For Boeing (through the 787) and Airbus aircraft (through the A350) both the over-pressurization and negative pressure valves operate completely independent of the pressurization system control circuits or manual cockpit commands and both rely on local, independent pressure data to drive their respective operation.
They are always purely mechanical devices, locally controlled for safety and reliability, although there are sometimes monitoring switches for cockpit indication of valve operation. For some aircraft, these valves are combined into one unit. The negative pressure valve is very often a very simple device - a spring-loaded door.