Just a general point - and I don't know if it applies here, but "square wave DC" could describe a series of +270 Volts "Direct Current" pulses, with an equal mark space ratio. In other words, the voltage is switched on/off/on/off etc. between +270VDC and zero volts.
True "alternating current", AC, alternates the polarity every half cycle; so on the first half cycle the voltage rises from zero volts to maximum positive voltage and back to zero. In the following half cycle the voltage changes polarity and goes to maximum negative voltage and back to zero again. The AC wave form is symmetrical around zero volts, i.e. it goes from zero - max positive volts - zero - max negative volts, and repeats. What 'Square wave DC' means to me that it is only ever between zero and positive voltage.
Normal AC voltage is a sine wave, owing to being generated by a physically rotating generator. Square wave is produced by electronic switches, and goes from zero to maximum (near) instantaneously, giving the classic square shaped waveform.
Many DC motors now work from square wave DC. This gives higher starting torque, good low speed response and lower heat in the windings. The mark-space ratio can be modulated for varying loads on the motor; the 'on' time of the square wave being very brief for light loads, much longer for heavy loads.
Your battery drill probably uses variable mark-space ratio square wave DC drive, and on some you can hear the high frequency of the square wave generator as you slowly pull the trigger.