There is a question on the form that he/she will need to answer yes/no about military discharges. He/she may not know what to put down. A false answer would be a felony.
Well, that question on the application here:
https://www.co.forsyth.nc.us/sheriff/documents/ConcealedHandgunPermit_Application.pdf
is, "Have you been discharged from the U.S. Armed Forces under conditions other than honorable?"
The answer to that question with either a regular Honorable discharge or a General discharge would be
NO.
The OPs question had nothing to do with him wondering what type of discharge of he has. He stated the fact, "I have a general discharge." He was asking what the requirements for a NC CCP are. There isn't anything to ask the State Bureau of Investigation about. A general discharge does not, according to state law, prohibit one from obtaining a CHP.
In fact, North Carolina's CHP requirements are more strict than Federal law, because Federal law only prohibits those with dishonorable discharges. A dishonorable discharge requires a court martial. An Other than Honorable discharge only requires an Administrative Separation Board.
My guess is the OP's situation went something like this, "OK, you did something stupid and we are going to kick you out of the Army. So here's your choices. You can just voluntarily take a General discharge and be done with it. It means you won't be able to come back in, you lose your GI Bill and that's it. Or you can go to an Administration Separation Board and they can recommend one of four things. You are not guilty, drop all punitive actions. You are guilty, but does not warrant separating you, retain in the Army. You are guilty, it does warrant separation, but only administratively (General discharge). You are guilty, and it warrants an Other than Honorable Discharge - which is just one tiny step above a felony."