Not sure about other agencies, but this is from the NACD website: NACD Training
The biggest difference standing out to me is circuits and traverses.
Apprentice to Cave
Although the NACD strongly supports and encourages the four-day Full Cave Diver course, it recognizes that some students may benefit from a program that provides for two separate two-day courses to attain the Full Cave Diver level. The Apprentice Cave Diver course is taught in a minimum of two days with a minimum of four dives in double cylinders. The emphasis of this course is an introduction to jump and gap procedures and continual improvement of the procedures, skills and emergency drills previously presented at the Cavern and Intro to Cave courses.
Full Cave
The cave diver course is one of the most advanced certifications available today. It is taught in a minimum of four days with a minimum of eight dives. The emphasis of this course is equipment configuration, decompression problem solving, jumps, circuits, traverses, and surveying.
The biggest difference standing out to me is circuits and traverses.