Amplifier: An electronic device which increases or boosts the power of the signal is called is an amplifier. I.e. both quantities of the signal (voltage and current), increases in amplifier. If it is voltage amplifier also there will not be decrease in current.
Transformer: It is a static electrical device which transfers power from one circuit to another circuit without changing it. Even though the signal quantities (voltage and current) can be boosted at the output, it cannot acts as amplifier because if one of the quantities is boosted at the output the other quantity is reduced. So the power is same.