Lutfij above is quite right. Some additional info.
There are two dominant major types of lighting devices used now - that includes both light strips and lights in fan frames. They are different enough that you can NOT mix the two on one circuit. So the lighted FAN you buy must have the same type of lights in it as the mobo lighting HEADER used to power and control them. Note also that all such fans really are two device in one unit - a fan motor, and lights - that are separately powered and controlled. Hence they have TWO cables to plug into different headers. One of these is for the fan motor.
For the LIGHTS, the simpler system is called just plain RGB. It uses a connector with FOUR pins on it - a common +12 VDC supply, and three separate Ground lines for the three basic LED colours on the light strip. Along the strip, all the Red LED's are connected to the one Red Ground line, and same for Greens and Blues. The lighting Controller manipulates those three Ground lines to generate thousands of colours. At any single moment the entire light strip is one colour, but that colour can change over time. Photos of such fans will show each with one colour over the whole fan. When connecting items in this system, you MUST match up the marked 12 VDC pins on the two connectors.
The more complex system is called Addressable RGB or ADDR RGB or ARGB or Digital RGB. It uses a connector with THREE pins (looks like it had 4 pins but one is missing), and their arrangement means you can only plug them together one way. The pins provide common +5 VDC and Ground lines, and a Digital Control Line. In the light strip, all the LED's are grouped into Nodes. Each Node contains one LED each of the three colours plus a small controller chip. All the chips listen to the Control Line and respond only to instruction data packets with their unique address, then do as they are told for their trio of LED's only. Thus at any one moment all the Nodes along the strip can be different colours, and of course those can be changed. So such a light strip (or frame) can have a rainbow of colours, and the rainbow can chase itself around, etc. Photos of this light type always emphasize this feature by showing rainbow effects.
Because both the Voltage used and the method of colour control is so different between these types, you cannot mix them on one circuit. I'll also draw your attention to another compatibility issue. The major makers of light strips and lighted fans now use particular connector designs that are "standard" so you can mix makers, but not the two types. However, there are other makers who use their own less-common connectors and that makes mixing those items with others, or with your existing mobo headers, tricky. Some makers offer adapters for this issue, but many do not. However, you can buy a set of components from one maker that does all you need if you do not plan to use components from another.
Note a possible source of confusion. Fan MOTORS come in two types - the older 3-pjn type controlled by voltage supply, and the newer 4-pin PWM type. LIGHTS also come in two types often labelled as either 3-pin (ARGB) or 4-pin ) plain RGB). So the LABELS appear to be the same, but there really is NO relationship. Any 3-pin fan (motor) could have NO lights, or 3-pin ARGB lights, or 4-pin plain RGB lights. And the same for 4-pin PWM fan motors.
For your query, OP, either type of lighting system can produce a custom colour in a fan frame. That is done by setting options in the control system. If you want the entire fan to be one colour at any moment, either type can do that. If you want to have multi-colour rainbow effects at any one moment, only an ARGB system can do that.
What it more important for you, I suspect, is to start with the mobo you have. Does it have a lighting header or not? If yes, of which type? Mobos can come with NO lighting header, with one type only or the other, or with some of each. If you tell us what mobo you have - maker and exact model - we can look up its details and help you to understand your options.