The lugs and receptacle are on 2 separate circuits in a sense. if the generator is showing power on the gage and no output from the receptacle, first thing I'd check is the GFCI reset on the face of the breaker.
If that is not tripped, then check the circuit breaker switch for the receptacle inside the control panel on the left side of the panel opening.
I'd suggest troubleshooting the receptacle first and the lugs 2nd.
Also, please tell us answers to all Guy's questions.... that will point us in the right direction, especially the last question, does the green light above the AC circuit interupt switch illuminate then you push up on the switch AND does it illuminate when you press in on the face of the light itself ( bulb test function )