They are both specified in volts AND amps. Both are necessary.
The service wires are 240 volts split phase, 120-0-120 volts, at 100 or 200 amps. Older houses could have 30 or 50 amp service. You have 120 volts from each neutral to the phase lines, and 240 volts phase to phase.
Branch circuits inside a house are of several types.
Most are 120 volts 15 amps or 120 volts 20 amps
The ones for high power appliances are 240 volts, 30 or 40 or 50 amps.
As you can see, they all have a voltage and current specification.
Note that some very large houses, apartment buildings, small businesses may have 208 volts 3 phase service, or even 410 volts 3 phase, but that is a different discussion.