I'm going by memory on the dates, but I'm pretty sure the order of models is correct:
1964 - First model 444 introduced; this had a straight buttstock with montecarlo cheek rest, barrel bands, 24" barrel, and rounded lever
a couple years later - Second model 444 introduced; lever changed to square
a couple years later - Model designation changed to 444S (sporter), buttstock changed to pistol grip, barrel shortened to 22"
a couple years later - barrel bands replaced with foreend cap and dovetail hanger
a couple years later - Model designation changed to 444SS (sporter, safety), crossbolt safety added
a couple years later - Model designation returns to 444, barrel changed from 1:38" microgroove to 1:20" ballard rifling
2000-2004? - Model 444p Outfitter introduced, straight buttstock, 18 1/2" ported barrel
So as you can see, there have been a lot of variants! As bcsteve mentioned, MO is a great forum to read about the 444.