No official NSS definition.
"Wild caving" is the term used for caving in passages that don't have wired-in lighting, and paved or otherwise developed trails, and which required special skills and equipment. Except in the easiest of caves, a person on a wild caving trip would need at a minimum a hard hat, light, and clothing appropriate for crawling, climbing, and traveling through mud and/or water. Some commercial caves offer "wild" trips that take visitors off the paved, lighted, trails through "real" cave passage. Of course cavers in non-commercial caves are "wild caving." And some cavers are "caving wild."
Cheryl