No, you’ve got the highlights exactly right.
In the NG or equally in the original or now modified MAX, a single AOA failure (hard-over actually, where the thing goes off-scale high or low, not just “a little out of tolerance”) produces noisy false warnings, misleading instrument readings, and plenty of opportunity for cockpit confusion.
The original MAX added one more thing to the mix. For an off-scale high failure, the original MAX would, via MCAS, mistakenly crank in big doses of nose down trim repeatedly and would not quit mistakenly trying until disabled.
Which meant that from the pilot POV, what had been a pretty darn confusing failure in the NG added runaway nose down trim to the mix in the original MAX. Which difference took a basically stable flight situation albeit with confusing instrument readings and made it into a very unstable flight situation on top of the confusing instrument readings.
Which super-confusing very time-critical situation duly got away from those two crews, but not from a different Lion Air crew who had had the same malfunction in the same jet the day before.
The modified MAX fixed that; MCAS will ignore off-scale readings, and if it does mistakenly trigger for an out-of-tolerance reading, it won’t do so repeatedly nor to excess. Thereby all-but neutering the runaway instability. Leaving us with a failure scenario substantially the same as that of the NG.
As to why MCAS?
Every airliner with wing-mounted engines has the issue that as you raise the nose higher and higher versus the airflow, those engines get more and more sideways to the airflow. In a sense, the incoming air gets “under” the engines and helps to push the nose higher and higher. Which could, at least in theory, lead to a runaway instability.
By regulation, every airplane has to be designed so that as the nose gets higher, it has to “feel” heavier to the pilots. It can’t begin to feel lighter as the situation gets more extreme. And it darn sure it can’t get so extreme that the airplane starts to pitch up on its own as more and more airflow gets under the forward-mounted engines.
In the case of the NG, the natural aerodynamics of wing shape, engine shape, CG, tail size, etc. means the airplane meets that pitch feel design standard. Barely. And even then the NG has some other gizmos to make it physically harder for pilots to inadvertently pitch up into a stall. IOW, the pitch “feel” is already artificially enhanced on the NG. As it is on many traditional airliners.
In the case of the MAX, the engines being a bit bigger and a bit farther forward on an otherwise almost identical wing & fuselage meant the MAX did not naturally quite meet the design standard. The extra pitch-up tendency due to the different engines ate all the tiny margin the NG had, and then some. And the limitations of the feel enhancement systems on the NG meant they couldn’t directly be cranked up a smidgen to make up the shortfall.
So MCAS was invented to give that little extra nudge at the right time to make the feel meet the standard. Actually, MCAS wasn’t invented for the 737; it was borrowed.
It turns out every 767 ever flown has the same MCAS augmentation to meet the standard. Because the 767 aerodynamics don’t quite meet the standard without some help from the pitch trim. And never did from Day 1.
The big difference between the 767 & 737 is the 767 has triple redundant everything with some majority voting and cross-sensor averaging, whereas the 737 whose design origins are 15-20 years earlier, has dual independent everything with the pilots meant as the one and only tie breaker for any disagreements.
The full implications of that different redundancy environment wasn’t fully appreciated by the various departments at both Boeing and FAA involved in the change. So MCAS was released with a vulnerability to a single point failure that was misjudged as minor but proved in practice to be severe.
The later Boeing 777 & 787 and all Airbus products have the same underlying concern and have equivalent fixes to the unhelpful natural aerodynamics. But those airplanes being fly-by-wire from beginning to end, the “fix” may have a name in the internal software documentation, but it isn’t a separate black box in the belly. It’s just one more parameter that goes into the software’s decision logic and results as seen by the pilots.
That’s quite a story!