Well, I'll bite, what is the difference? I'm a certified teaching pro who has played (still play) and taught (still teach) for quite a while.
I can relate, as I've been teaching over 20 yrs and was USPTA certified as well. Most of that time I was teaching conventional and working with other conventional coaches, so I'm very familiar with both sides of this.
There are certain fundamentals used in conventional that may be denied, but are common.
Neither approaches are stance dependent, but first leaned is very important to development.
1.MTM starts with open instead of Neutral or closed. (very important for balance and court coverage as the game speeds up)
2.MTM teaches to find the ball from below with timing for topspin, then at contact to accel up and across the ball to an over the shoulder finish.
Conventional teaches to accel the swing into the ball and finish out thru the ball towards the target. (this maybe too subtle for some, but it is the biggest thing IMO. )
3.MTM prepares early by moving to stalking positon, then a focus on waiting and timing, but
conventional talks of getting racket back earlier when the game gets fast.
4. MTM teaches the slice much the same, but find the ball from above, than at contact to pull down and across.
5. MTM teaches to point the butt cap at the ball at the start and finish of the stroke, pulling the racket towards the contact, then presenting the strings with the change of direction of pulling up and across.
You can see RL in his vid, how his racket stays much inline with his forearm, which is why he talks of driving the racket, pushing instead of pulling the racket.
These are not everything, but just several of the basic differences. The beauty is the lack of compensations that are required by the conventional. Half your time when coaching conventional is teaching how to hit harder, but without hitting in the net or long. This does not happen with MTM as players can hit harder and harder as their feel gets better without problems with the net or long. Even very avg talents blow right thru 3.5 and 4.0. Hitting harder is just about getting more comfortable with the stroke and feel. The technique encourages more control as the swing gets more powerful. Sort of inverse from conventional instruction.
When a MTM player steps forward/neutral, it is for contact point and usually not to gain momentum (cause none is needed/power is abundant already). IF they continue on in with the shot it will be balanced and just to transition on in, not for momentum.
IMO, if you are teaching these MTM things you are not teaching conventional and should not be insulted. If you do believe in conventional and teach it fine, do what you believe in, but why get defensive if you really believe. If you are teaching some of both, fine, but realize you have a foot in both boats and have choosen what you believe in.