i think theres a problem here with the jargonYes it does. A medium cage x.9 will only take up to a 32t on the cassette, while a long will do 34t. Brand doesn't really matter, but size does.
a longer cage will make the derailleur take up more slack, thats what you guys keep referring to.
the pulley and body design is what makes the derailleur be able to reach a larger sprocket, and in thise case that doesnt change between the long and med cage versions.
the number you are referring to is the max. difference between amount of teeth, that the derailleur can still take up slack in.
for instance if you have a 12-34 setup, and a 22-32-44 setup, then if you use the 34 cog and 44 ring, youd be using 78 teeth, and if you use the 12cog and 22ring you would be using 34 teeth, meaning your derailleur would need to take up 78-34 teeth of slack which is 44, outside of range. but since you never go smaller than 16t on the 22ring and never bigger than say 24 on the big ring, your maximum needed tension capability drops back to 28 which can be served by a mid cage derailleur, now factor in a chain growth on a dual suspension bike of the equivalent of 2 teeth and you have 30.