I agree with bodhitree.
Fighting is fighting. Period. Whether it's "MMA" or "CMA" or two guys with no training trading blows. Whether somebody is thinking about kicking another guy in the nuts or not.
Self-defense INCLUDES fighting, but is not limited to it. Self defense includes things like awareness of your surroundings, studying human "give aways," like posture, facial expressions, etc, understanding what is safe and what is not, de-escalation techniques, and a fair bit of psychology I would guess.
You could be great at self-defense and a lousy fighter. You could be a world-class fighter and lousy at self-defense.
To me, the MMA/CMA argument is a pointless one. It doesn't actually mean anything. The real issue is training. If you are training hard, and suit up and beat on each other on a regular frequent basis, you're probably going to be effective.
"In the world of martial arts, respect is often a given. In the real world, it must be earned."
"A stupid man's report of what a clever man says is never accurate because he unconsciously translates what he hears into something he can understand. "--Bertrand Russell
"Liberals - Cosmopolitan critics, men who are the friends of every country save their own. "--Benjamin Disraeli
"A conservative government is an organised hypocrisy."--Benjamin Disraeli