A common emitter BJT amplifier has the emitter grounded. It may be directly connected to the ground or it may be connected through a small emitter resistance. The resistance decreases the overall voltage gain, but increases stability. This resistance is shorted in the AC equavalent circuit by using a emitter bypass capacitor. Any amplifier circuit where the emitter is directly or through a resistor is connected to the ground is a common emitter amplifier. So why is it called a common emiiter amplifier ? You measure the input voltage at base with respect to ground. You measure the output voltage at collector with respect to ground. But the emitter is the ground. So both the input and output circuit have the emitter as common. So it is called a common emitter amplifier. Hope this was helpful.