Pwm is a pulse modulated fan. It's a constant 12v on. To control the rpm, the pwm signal turns the fan on/off many times, so at anything less than 100%, it'll be in a constant state of trying to turn on full. That's 4 pin, 12v hot, ground, rpm tach and signal wire. You can get fans that'll range from @18% speed to 100% speed.
3pin is analog, it's voltage controlled. The higher the voltage, the faster the fan. Good fans will handle @5v, normal fans @7v at lowest, so fan ranges are usually @40 (60)% speed to 100% at 12v.
Thats power. On top of that are 3 basic fan designs. Ball bearing, sleeve and hydraulic. Then you have single/double ball bearing, in sleeve there's sleeve, rifle etc and in hydraulic there's even more, basically 2 types (as per patent) but every brand has its own name for their own design of hydraulic bearings.
So it's possible to have a 4pin sleeve fan or 3pin hydraulic, or 3pin sleeve or 4pin hydraulic. The bearing type is separate from the power type.
For simplicity, if the motherboard has a 3pin fan header for the front fans, you need a 3pin fan. If it's a 4pin header, you can usually use either 3 or 4pin, however, 3pin run much faster at lowest settings and the led brightness will dim out with lowering the voltage to lower speeds. 4pin pwm fans are constant voltage so leds are always the same brightness no matter the speed.
Hope that helps a little.
Edit: generally for a good fan, @900rpm is still very quiet. 1200rpm is quite noticeable. 1500rpm is a drone that can be heard even with headphones on. 2000rpm is loud enough that talking in loud voices is necessary.
If you have a 3pin led fan capable of 2400rpm, it'll not turn down at pc idle much beyond 1100rpm and the led will be out. A cheap 3pin and you are looking at 1400rpm at best lowest. The same fan, pwm will probably see @450rpm at lowest, which is basically silent. Big difference. Use pwm when possible unless noisy fans don't bother you. (or anyone else)