It's two sides of the same coin. Moving the (larger) engines forward from under the wing affected/changed the stability of the aircraft. The most relevant change is that at low speed and at a high angle-of-attack, the new dynamics of the aircraft would cause it to continue pitching upwards, potentially resulting in a stall. (This degree of AoA was more than would be encountered in normal flight, and there wasn't a danger with the old under-wing engines anyway.)
MCAS was designed to stop the pilot pulling up into a very high Angle-of-Attack by adjusting the trim to pitch the nose back down, but the fact that each MCAS system only had one AoA sensor means that in two instances the system started pitching down even when the plane was level, and "corrected" the plane back to the ground.
(As you described, there was a desire to keep the new plane as similar as possible to the previous model, so a lot of these changes were glossed over.)