and this is where the divide begins.
i know for a fact of practitioners that are in their 60' and 70' that would, could and have, beaten the snot out of men in their 20's ands 30's in real street confontations. but when you start down the road of magical chi and fu fu dust powers, you lose me. i fully understand the difference between altheticism and martial skill. combative skills can continue to improve as we age but there is no getting around the fact that we age and our overall ability deteriorates. people often talk about great masters who can do all kinds of amazing things and i can tell you i have met a good amount of these "masters" myself and i know others who have gone to china and had the rare oportunity to "cross arms" with many of the great masters there as well...but there is no getting around the fact that it is not magic and all abilty can be attributed to bio machanics and skill. if you believe otherwise that is ok but i have seen too many instances where the ones who claimed to have that "something more" failed to be able to show it when asked so you will have to pardon my skepticism.
the op asked the difference between TMA and MMA, i dont think the argument about chi is fitting for this thread so lets just say, in TMA there are those that believe in chi and internal strength and in MMA in general they do not.
from my point of view the difference is in scope of vision. you have practiced and worked out for many years and you can beat up the world, lets say you are an unstopable super hero...NOW WHAT? so you can beat up anyone who stands before you, so what. you spent 20 , 30 , 40 years of your life for that? as someone once told me as a young man your still a scared little boy inside who fears the world and has a need to be able to fight and defend themselves against the boogie man. then as we age at some point we are not scared little boys anymore. there should to be a larger vision on why we train if you plan on continuing as we get older. TMA provides this while MMA does not. my cousin was a supurb male gymnast. he is in his 30's now and i asked him if he ever practices anymore and he looked at me like i had 3 heads and said "if your not compeating. what would be the point? why would you put your self through that if you were not compeating?" the same hold true for MMA. men like Randy couture, Gracie, ice man and ace franklin have a hard time admiting that its time to retire because in MMA when your done your done. there is not point to it after that.