Amplifiers are usually named for their primary role.
The primary task of a voltage amplifier is to increase the voltage of a signal, so they are referred to as voltage amplifiers, even though they often amplify the power of the signal as well.
The primary task of a power amplifier is to provide power to drive a load, such as a speaker or an antenna, so they are referred to as power amplifiers, even though they often also amplify the signal voltage in that process.
Voltage amp amplifies voltage, but the output current might be limited.
A power amp tries to keep the output voltage constant over a wide range of loads.
Current amp amplifies current, but the output voltage might be limited.
A current amp tries to keep the output current constant over a wide range of loads.