Noise match is used for minimizing "Noise Factor" of an amplifier and gain match is used for maximizing the gain of an amplifier. However, for achieving a good noise factor for a multistage amplifier, you should you should consider noise match and gain match simultaneously. Power match is totally different from noise match and gain match in amplifiers and is used only for power amplifiers. You can learn matching details in the "Microwave Transistor Amplifiers" By Guillermo Gonzalez.