In practical terms, the major difference between 3-pin and 4-pin fans comes when you mis-match a fan type with a header type. But almost all modern mobos have an option you can use to solve this. The two fan types require different methods of how a fan speed is controlled. For 3-pin fans, the only way is to manipulate the VOLTAGE supplied to the fan from the header on pin #2. For 4-pin ones, that voltage is always a full 12 VDC, but the header supplies also a new signal called PWM from Pin #4, and THAT allows the fans speed to be controlled. If you connect a 4-pin fan to a header using the older method, its speed is still controlled, but not quite in the best way. But if you connect a 3-pin fan to a header using the new method, that fan always runs full speed.
In BIOS Setup, when you get to the screen to configure the details of how each header controls its fan (you do this for each header separately), you can choose to use either the older Voltage Control Mode (aka DC Mode) or the new PWM Mode. So you merely need to set that to match the type of fan connected to that header. For this reason, IF you are using several fans on one header via a Splitter, do NOT mix fan types on one header.
On all mobos there are two slightly different groups of fan control headers. In the default automatic control scheme, ALL of them are based on changing the fan speed according to a TEMPERATURE measured by a relevant sensor. For the CPU_FAN and CPU_OPT headers, the sensor used is one built into the CPU chip itself. For the general case ventilation fans connected to SYS_FAN or CHA_FAN headers, they use a sensor built into the mobo. On SOME mobos there may be additional sensors on the mobo for specific components, and you MAY choose to use one of those it you are doing special cooling for one of those particular mobo components, but that is not common. So, it make perfect sense to connect all fans associated with CPU cooling to the CPU_FAN header, and all case ventilation fans to any of the SYS_FAN or CHA_FAN headers.
On most mobos, the PUMP header does NOT have any fan speed control capability. It is intended to power a pump in a liquid-cooled CPU cooler system. In most of those systems, the pump is always run at full speed, and control of CPU cooling is done solely by changing the speed of the fans on the radiator. So the PUMP header does NOT try to control the speed of its device.