Actually, CIC and CCI are international classes run by the FEI. National events run by BE are offically known as "CNC"s.
CICs are international one day classes, whereas CCI are three day classes with the showjumping last and a longer xc course. However, with the introduction of the short format, some argue that the differences between the two classes are now fairly small.
A national novice class run by BE is the equivalent of a CCI/CIC*, intermediate = 2*, advanced 3* and 4* considered the 'ultimate.'