Does a 230 V (240 V) single-phase motor technically draw twice as much current as the label states?

A 240 volt motor will only be connected to the two live wires, not to neutral, so your example draws 6.6 amps at 240 volts. If it is connected to operate at 120 volts, it will be connected between one live wire and neutral, and will draw 13.2 amps at 120 volts.

I think it is misleading to say that, in the 240 volt case, the motor draws 6.6 amps from each live wire. A more correct description would be that it draws 6.6 amps from one live wire, and returns that 6.6 amps through the other live wire.

Using the same terminology, in the 120 volt case, the motor will draw 13.2 amps from the live wire, and return that 13.2 amps through the neutral wire.

It is written in a confusing way, but well. The one phase motor has only one phase from which something is drawn, the other one is bound to ground. You use a one phase motor because you don't have three phases. That means using phase-phase voltage on it wouldn't make sense, you should be using a three phase motor instead.

The 120V vs. 240V is not related to phase to phase voltage(or live wire to live wire) as that would be \$120\sqrt(3)\approx 207V\$. It is a refference to the outlet voltage for different countries. You have:

• 120V 60Hz (for example US)
• 240V 60Hz (for example Brazil)
• 240V 50Hz (for example Europe)

The other ratings you read were for people in other regions of the world that want to use the same motor.

You need a bit more of data in the question, and clarify it so that I really know what you are talking about. I'm now doing my best guess at what you really wanted to ask.

You can think of it this way: the motor is using the same amount of power regardless of the voltage. From your formula, you know that since the voltage doubled, the amount of current flowing through the wires and motor must have halved, since the power is the same.

This is also the reason devices that are switchable for 120/240 volts use a fuse with half the current rating of the 120 volt setting when set for 240 volts.