If you pull the wire loom off of the solenoid pigtail you'd see the following:
Solenoid -> 4 wires -> Relay -> 3 wires -> black connector
You would cut the 4 wires between the solenoid and relay. The way these solenoids work is that there are two separate solenoids in one. Green + White wire makes one circuit, this is the high current "pull" solenoid. White is power and green is ground. This circuit should only be energized for about 2 seconds, just enough time for it to actually pull the flappers open. There's also a low current "hold" solenoid, red is power and black is ground for this circuit. This one doesn't have enough power to pull the flappers open but does have enough to hold them open after the "pull" solenoid does it's job. This circuit is designed to be energized as long as you want the flappers to stay open.
My understanding is that your existing system (I'm assuming with the white 4 wire connectors) and the newer style system (with the 3 wire black connectors) both operate identically. The difference is that in your style system, the time delay relays (which are responsible for powering and then cutting off the "pull" solenoid after 2-ish seconds) are built into the harness that's wired into your boat, whereas the new style system has the time delay relays built into the pigtail on the solenoid to simplify replacement.
