Each agency has their specifics as to what standards they use. Most have some commonalities, enough that it is difficult to determine which is which but comparable
From the NACD standards:
LIMITS:
A. Natural sunlight.
B. Maximum 200 feet penetration distance.
C. No decompression diving.
D. No restrictions.
E. Maximum depth - 100 feet.
F. Minimum visibility - 30 feet.
G. Minimum starting psi - 2000 psi or 50 cubic feet.
H. 1/3 air rule on singles, 1/6 on doubles.
10. MINIMUM EQUIPMENT:
A. Mask, low volume type recommended.
B. Power fins-straps taped together, if applicable.
C. 72 cubic foot or greater single cylinder. Recommended: Single cylinder with dual valve orifice.
D. Single hose regulator with an octopus as the alternate air source and submersible pressure gauge.
E. Exposure suit, suitable for diving location.
F. Buoyancy compensator with auto inflator, C02 devices rendered inoperative.
G. Submersible dive tables or computer must be used
H. Knife, preferable small and sharp, or line cutter acceptable to instructor.
I. Slate and pencil.
J. Watch or bottom timer and depth gauge. A dive computer may be used in place of these.
K. Weight belt or other instructor approved weights.
L. Battery powered dive lights, at least two per diver. These lights should have a suitable burn time for the dive being planned.
M. Minimum of one safety reel per diver.
N. One primary reel per team.
Note that an instructor can ask that you have additional equipment such as a second safety reel/spool, a long hose and a second cutting device
The definition of the cavern zone as per NACD is :
For training purposes, cavern diving is defined as that portion of the cave environment illuminated by natural sunlight which has no restrictions, is not deeper than 100 feet, does not exceed 200 linear feet from the surface entrance and has a minimum starting visibility of 30 feet. There is no cavern diving at night.