Hi Ben,
GP answered your question pretty well. However, you asked about Intrastate(within the same state) transactions. Feds are not involved with intrastate transfers. In many states private sales may be shipped directly to the buyer. The Feds get involved in Interstate(between two states) transfers. In my state(Utah), having a CC permit eliminates the need for a background check in either type of transfer. Receiving a gun interstate however, must involve an FFL holder to receive the gun and to complete the legal transfer. Here, the FFL must call to confirm that my CC permit is still valid but the background check is not necessary.
