They're just different control units. BB, or Black Box, is the name for the previous power base because it is a very simple box shape, and it's black. It also has less features in that it is essentially just a box that facilitates car control. In order to have lap counting or even a computer interface for race management, you need another accessory, the Lap Counter. There are other accessories as well, but that would be the minimum.
The CU, or Control Unit, is the name for the new power base, which has a more modern design with an arch of LEDs above the bit with all the buttons and switches. It has a built-in communications port for connecting to a PC, or for their App Connect device which provides a bluetooth connection for smartphones and tablets to use race management programs on. The CU needs only a PC adapter cable, or the App Connect device, to be able to be controlled by a race management program. No other Carrera accessories are required.
The CU also has an option that allows it to handle fuel calculations, whereas the older versions put that duty on the car chips. This allows for more realistic fuel load simulation.