Can any 2.4 GHz transmitter work with any receiver?

This is a thought you would have, especially if the receiver of your RC car is 2.4 GHz and you need to use another receiver with it. Unfortunately, 2.4 GHz receivers cannot be interchanged. ... 

Another reason is the variance of brands; 

2.4 GHz receivers will only work with 2.4 GHz transmitters of the same brand.