Stability and motion control.
When you walk, your foot rolls slightly inward as it lands. That is normal. If it rolls inward too much — overpronation — the arch collapses and strain travels up through the arch, shin and knee.
A stability shoe is built to limit that motion. A neutral shoe is not; it only cushions. Getting this wrong is why expensive shoes sometimes feel worse than cheap ones.
Stability shoes aren't all the same. Modern guided designs and traditional medial posts solve the same problem in very different ways.
The question isn't which is most cushioned. It's whether you need a stability shoe or a neutral one — and most people don't know which they are.