Well allow me to state some of the many differences existing among both amplifiers and transformers.
As their names imply, the first amplifies the signal (voltage, current, power) while the other transforms the signals characteristics i.e. voltage and current.
A transformer steps up the voltage, but then it steps down the current so the power is the same on both primary and secondary sides.
An amplifier on the contrary steps up all 3, voltage , current, and power, because it's connected to a DC supply which can help add some power to the signal.
A transformer depends on the magnetic field coupling both primary and secondary coils, and thus tranferring energy between both sides. While an amplifier doesn't operate with magnetic fields, it mainly depends on semiconductor devices that have 3 terminals, and depend upon the motion of charges in them between these 3.