The max current stays constant whether 4 or 8 ohms (assuming the output transformer has both taps) but the max voltage changes. An 80 watt tube amp will deliver the same watts & current to both a 4 ohm or 8 ohm speaker, but the 4 ohm speaker will get double the voltage.
Not exactly, max power stays the same but both voltage and current change.
The 4 ohm doesn't get double the voltage of the 8 ohm, that would produce 8 times the power.
The 4 ohm gets .707 of the voltage that an 8 ohm speaker gets and draws 1.414 times more current. This keeps the power the same for both.