In case you are interested... a Natural Area is just an area of State Park Service-managed land that is set aside for additional protection. Presumably because it has some interesting or unique plants or animals inside.
N.J.A.C 7:5A is more of a template, but each Natural Area has similar rules restricting what the Park Service can do there. It doesn't really affect people like you or me. We can still walk or hike through it, if there are trails or roads. I guess most Natural Areas are also open for hunting, fishing, and trapping. (Bass River State Forest's Absegami Natural Area is closed to hunting, but not because it is a Natural Area - it's just too close to the campgrounds and swimming area.)
If you think of a linear scale with "more preservation" on one end, and "more recreation" on the other, Natural Areas are way over on the preservation end. Campgrounds and day use (swimming) areas are over at the recreation end. Other State Park Service lands are in the middle.