Starting point: Any 3-pin fan can ONLY be controlled by a mobo header that is using Voltage Control Mode (aka DC Mode). It cannot be controlled by a header using PWM Mode. 4-pin fans can be controlled by EITHER type of header, although a true PWM Mode header is preferred for them.
So how do you tell about headers? Well, ALL SYS_FAN or CHA_FAN headers with only 3 pins can only be Voltage Control Mode. If your mobo header has 4 pins, that does NOT tell you what it does. I have seen three types of headers that all have 4 pins:
(a) True 4-pin header that uses only PWM Mode - suitable only for 4-pin fans. A 3-pin fan on this header will always run at full speed.
(b) A 4-pin header that has options in the BIOS Setup screens to be set to operate either in PWM Mode or Voltage Control Mode. These have good flexibility and can control either type of fan. In fact, since 4-pin fans CAN operate and be controlled by Voltage Control Mode, any fan can be connected if this port type if it is set to Voltage C0ontrol Mode.
(c) a 4-pin header that has a useless 4th pin and really ONLY operates in Voltage Control Mode. Because both fan types can be controlled by this mode, the headers seem to be "universal". BUT you cannot use them with Fan Hubs (which can only be done in a 4-pin header and fan system), because such Hubs REQUIRE a PWM signal from Pin #4 and this header type does not provide it.
Sometimes you can tell which type of header you have from your manual, sometimes not. Usually ones that are 3-pin only, or 4-pin true PWM only, or configurable in BIOS Setup are made clear in the manual.
OP, if you post your mobo maker and exact model number, we can try to figure out your header type.
By the way, there's some misinformation above about the signal on the header pins. On a 3-pin fan, Pin #1 is Ground (Black wire), Pin #2 is the +VDC supply varying from 5 to 12 VDC to change the fan speed (Red wire), and Pin #3 carries a pulse signal (2 pulses per revolution) generated by the fan motor back to the header for counting to display speed AND to monitor for fan failure. This signal is NOT used for actual fan speed control. Fan speed actually is manipulated according to a TEMPERATURE sensor on the mobo (for case fans) or inside the CPU chip (for CPU cooling fans.)
On a 4-pin fan, the wire color codes are different, but Pins 1 and 3 are identical to the 3-pin case. Pin #2 is always the full +12 VDC (unlike the varying voltage for a 3-pin fan), and the new Pin #4 carries the PWM signal. Inside the 4-pin fan motor there is a chip that uses the PWM signal to modify how much time the current from the +12 VDC supply (Pin #2) is actually allowed to flow through the motor, and this is how speed is altered.
Now, many fans versus one header. You CAN connect more than one fan to a single header. It used to be limited to two at most, but today most fans draw much less current. Most mobo headers can supply up to 1 amp to fans, and many fans consume less than 0.2 amps. So theoretically, IF you check the fan current draw ratings, you could connect four or five "common" fans to a single mobo header. To do this you need a SPLITTER. These days you can't find 3-pin splitters, but a 4-pin splitter works both for those and for 4-pin fans. It's easy to find ones with two output arms, and often with three. You can plug splitters into a splitter; for example, 2 splitters into one splitter (two outputs each) can make four outputs. Four or more output arms on a SPLITTER is getting hard to find. You can find 4 and more arms in a different device, a 4-pin fan HUB. This device is different because it also has a special cable that must be connected directly to the PSU using one of its power outputs, and it can ONLY work if you have a true 4-pin header operating in PWM Mode, and are using only 4-pin fans.
Now, when you use a splitter to connect more than one fan to a header you won't be too surprised at this. If you have 3-pin fans, you can only CONTROL their speed with a header operating in Voltage Control Mode, no matter what splitter type you use. If you have 4-pin fans, they can be controlled by either type of header. You can even mix 3-pin and 4-pin fans using splitters, IF the header is in Voltage Control Mode.