Not sure, I thought - using terminology I've read about - it goes from weak inversion (not doing much, but can be useful for certain designs), to strong inversion (useful region), then at higher Vin reaches saturation (nothing changes with further increases in Vin).
Gain is maximized if everything is in saturation, but
you don't always get to say.
You say with certainty how a diff pair is designed,
but what you say is not always so. Sometimes a
P diff pair is better and very often a rail-rail input
will consist of both N- and P- diff pairs woven
together so when one quits working well, the other
has come around.
An N diff pair will go from cutoff (bad) to saturation
(good) to triode / linear (not so good) as VCM rises
from 0.