Generally speaking todays motherboards have 2 of the PWM headers for the CPU and any secondary cpu fan item (cpu-opt), these 2 connections are best used with PWM actual fans with 4 pin connections. Because the method of control is via PWM, the feed voltage is the same, so a 3pin fan will run at full speed.
It is true that a 4pin actual PWM connection running PWM (because sometimes you can switch in the MB bios/uefi to voltage control) will not fully control a 3Pin fan which has no PWM capability connected, YES. Because good pwm 4 pin fans even with quality parts are inexpencive , and because it will work the way it is, there is no problem using what you have , then upgrading it with a 4pin actual PWM fan when needed/desired.
Chassis (case not cpu) fan headers come in 3& 4 pin, but many (most but not all) of the motherboards do not use actual PWM for these "other" connections, so control of them does not "require" a 4 pin PWM fan because they will be voltage controlled anyway. They will still work with a PWM 4pin fan or a 3pin fan, either will be in a voltage control mode (not actual PWM).
So in the case of most of these cpu fans, you really prefer and many good coolers come with a 4pin connection and a real pwm operational fan. In most of the chassis connections you can also use a 4pin pwm fan, it just is not likely to be needed/expected like it is for the cpu fan items.
Some fans and cooler items come with an array of connections, for connecting more than one way. A 3 pin fan connection lines up on the 4 pin header just fine, and provided the voltage and rpm readings. A 4pin fan can also be put on a 3 pin header, and the voltage and rpm will still be correct. Either fan can be voltage controlled, a PWM fan though has additional capability to be PWM controlled. They were pretty good about using the best methods for cross compatability.