Basically my question is because I want to build a pc 100% compatible with Razer Chroma and be able to play with the lights, but the fans that I liked the most are Cooler Master, and both brands are not compatible with each other.

So if I buy AIO Cooler Master ARGB liquid cooling, should it work properly if I plug it into the Razer chroma RGB controller?

Barry summed it up well, that ARGB - Addressable RGB allows individual LEDs to be set to different colours, rather than RGB which is just all at once matching.
But due to differing hardware, and control methods, there is no guarantee that because it shares a name, that different components work together.
I've seen in various reviews many different connectors types, though typically the bigger brands tend to standardise more, particularly if they advertise compatibility across multiple motherboard… See More

Addressable rgb just means that the lighting can be set across multiple points on the same device instead of just all one color like standard rgb.

It doesn't matter what brand the devices or controllers are they are all cross compatible.

I have the fans and cooling block of my Cooler Master Masterliquid 360 plugged into the in built aRGB controller in my Deep Cool case along with 4 Deep Cool fans and its all works just fine.

As long as it says Addressable RGB Controller, it should work fine theoretically. Don't see any reason why it shouldn't.

#help