I believe MAMS the term stood for multi-axis, muzzle stability.
There was a time around 2010 where low flash compensators were the rage, that segment seems to have started with the 1957 Armalite AR10 sound, flash, and recoil compensator, which was a huge sound suppressor sized muzzle device compensator. The AR10 unit was probably inspired in part by the earlier FG42 compensator so it may be more accurate and less American to give the Germans at least partial credit for it. German arms technology in post WWII era was very closely studied by Aberdeen and the firearms industry. I met a firearms collector who’s father (an Army Ranger officer), was tasked in post WWII with gathering up relevant small arms examples and shipping them back to Aberdeen for study. Kac got at least some of their FG42’s from the Colt collection, evidence Colt studied it.
Knights made a spinoff I feel was related to the 1957 Armalite device for the Colt ACR rifle that the Army never adopted. The muzzle device was regardless an interesting piece of work.
They then made the Triple tap brake with Doug Olson, which was patented and miniaturized the functions of flash and muzzle rise compensation down to the size of the NT4 comp mount.
The battle arms development battle comp came out around 2008 or so (I can’t remember) and we made a comp with 90 degree holes around a time KAC made the mams. Our device was made on the theory of flow rates and the miners safety lamp, and our inspiration was the AR10 compensator, but our holes were .093” for manufacturability because tiny drills are problematic in manufacturing and our device was affordable and had to be for it to have any market relevance.
It seems that possibly the reason for the mams was the trouble of machining the TTB with the tiny slots. The mams however does not use holes 90 degrees to bore axis, it puts them in at a slight rearward angle, and that’s probably where (multi-axis) comes in. They are also smaller I believe, I don’t know what size exactly.
They dropped cost about 25-35% ish from the TTB to the mams, but it was still 2.5-3 times the cost of competing devices.
I haven’t fired a mams or a ttb, and have only seen the mams once at a trade show. It seems they are well liked, and they probably work pretty well.