The purpose of a voltage amplifier is to make the amplitude of the output voltage waveform greater than that of the input voltage waveform (although the amplitude of the output current may be greater or smaller than that of the input current, this change is less important for the amplifier´s designed purpose).
The purpose of a current amplifier is to make the amplitude of the output current waveform greater than that of the input current waveform (although the amplitude of the output voltage may be greater or smaller than that of the input voltage, this change is less important for the amplifier´s designed purpose).
In a power amplifier, the product of voltage and current (i.e. power = voltage x current) at the output is greater than the product of voltage x current at the input. Note that either voltage or current may be less at the output than at the input. It is the product of the two that is significantly increased.