I believe it's actually the other way around. DC fans need to change their voltage to change speeds, most DC fans operate from 5-12 V DC to get their full range of speed. PWM (Pulse Width Modulation) on the other hand maintains 12 V as the voltage, but it doesn't supply 12 V at all times, it sends pulses of 12 V to the fan and the length (or width) of those pulses determines how fast the fan goes. So a wider pulse will maintain 12 V to the fan for a longer period of time and increase the speed at which it turns. Most fans will only work with one or the other, that's why you would have to check what your mother board is capable of outputting. I got lucky in my case because my mother board can output both PWM or DC fan signals on the "CPU_FAN" fan header on the mother board.
What mother board do you have allkindsoftime?