What is the difference between a CB amplifier and CE and emitter-follower?

I think you mean a common emitter amplifier, which is an amplifier of voltage.
Emitter-follower or common collector amplifiers are used to match impedances, or to amplify power or current. The emitter-follower is a type of common emitter circuit that has a resistor between the emitter and ground. The output signal is taken from the point between the emitter and its resistor.