Excellent info above. Further note. The old fan came with TWO connectors on the end of its leads for flexibility, but you must use only ONE of them. The way it was done gives that fan a constant 12 VDC power supply directly from the PSU to run full speed all the time. The alternative is NOT to use that particular connector. You can plug the smaller 3-pin female connector into a mobo fan header IF you have one available and of the right type, and then it gets power AND automatic speed control from that header. But the "trick" is that the header must be of the 3-pin type, OR if of the 4-pin type you must be able to configure it (in BIOS Setup) to use the older Voltage Control Mode (and not the newer PWM Mode). A 3-pin fan like that can only run full speed if it is used on a mobo header using the new PWM Mode, and that is exactly the same as doing it as the old one is now - direct to the PSU.
Since you are buying a new fan, depending on what mobo you have and what headers it has for your use, you may need to stick with the 3-pin fan type, or you may want to switch to a 4-pin PWM type of fan. If you stick with 3-pin and plan to connect it again to that Molex power from the PSU, you do not need the extra smaller fan connector on the wires of the new fan.