For many recreational boats the waste pumpout is 1 1/2 inch (ID).
There may be other sizes and different adapters may be needed.
The pump out station system may have a push on fitting, that has a soft collar than jams into the pump out fitting on your boat, Those 'push on' fittings usually need to be held on the fitting to avoid the hose falling off.
The second type of fitting is threaded and screws into your deck fitting making holding the hose steady un necessary.
Both of the adapter styles have a mounting ring that is used to connect the fitting to the pump out station hose.
I also see that your boat is a Gulfstream. That model may have a portable head that has to be removed from the boat to empty
Can you determine the make and model of the toilet. A picture would help
