Both solid state and tube amps produce a voltage. Current is what results when voltage is applied to a load, such as a loudspeaker. An amplifier might be capable of high voltage output under no load condition, but if it has little current delivery capability this voltage cannot be maintained into a load. Your preamp typically can output a signal of several volts, enough to play a speaker quite loudly, however if you hook it up to a speaker I doubt you would hear anything. The preamp can only deliver enough current to maintain the voltage into a load of several tens of thousands of ohms, not 4 or 8 ohms.
Tube amps have high "rail" voltage (plus and minus 400 volts or more) so that the output tubes can apply a high voltage to the primary winding of the output transformer. The output tubes cannot deliver a great deal of current. However, the output transformer is wound with a step-down turns ratio, so that the secondary output voltage is down to a handfull of volts, as appropriate for the speaker, but the necessary current capability is there. You might think of the output transformer as similar to the gearbox of a sports car, which permits a small engine reved up to 7000rpm, to accelerate the car from a standing start.
Tube amps have high "rail" voltage (plus and minus 400 volts or more) so that the output tubes can apply a high voltage to the primary winding of the output transformer. The output tubes cannot deliver a great deal of current. However, the output transformer is wound with a step-down turns ratio, so that the secondary output voltage is down to a handfull of volts, as appropriate for the speaker, but the necessary current capability is there. You might think of the output transformer as similar to the gearbox of a sports car, which permits a small engine reved up to 7000rpm, to accelerate the car from a standing start.