The majority of NC Sheriffs use the Permitium online service to process their CCH applications. This service is free for the county sheriff but there is a "convenience fee" for the applicant. When the screenshot for the Wake County application on the left was taken, the amount paid to Permitium for your convenience was $4.
I'm assuming that the Permitium application is the same or at least mostly the same for all counties using the service. I also assume that using the Pentium online service is not required to process a CCH permit application and that the applicant can do so in person, at the sheriff's office. I have not validated these assumptions.
Contact your sheriff's office for definitive information about the CCH application process.
If you want to review the form before actually going to the site to fill it out, copy the image on the left to your local computer and use an image viewer to enlarge and read it.