Nobody can explain them.
A few years ago, at the height of the "model of the month" phase at S&W, they actually put out a decoding wheel to explain the four digit model numbers. There is (a little) logic to the system, maybe somebody remembers it and will explain. Me, I just look at the gun.
I don't remember where I found this or I would give credit where it is due, but I saved it for reference.
The first two digits indicate caliber:
39=9mm
59=9mm
69=9mm
10=10mm
40=.40S&W
45=.45 ACP
35=.356TSW
The third digit indicates model type:
0=standard model
1=compact
2=standard with decocking lever
3=compact with decocking lever
4=standard with double action only
5=compact with double action only
6=nonstandard barrel length
7=nonstandard length barrel with decocking lever
8=nonstandard length barrel with double action only
The fourth digit indicates type of material:
3=alum frame with stainless slide
4=alum frame with carbon slide
5=carbon frame and slide
6=stainless frame and slide
7=stainless frame with carbon slide
Also, model 39 was a single stack nine, where the 59 was a double stack.
Then came the 459, 559 and 659, with frames of alloy, carbon steel and stainless respectively. At least that's what I sorta recall from the early '80's.
Since this is in the revolver forum, I think the question was answered correctly in the first two posts.
Actually, the Model 629 is one that makes sense. We know the 6 means it's stainless. If you subtract 2 from the 6 so that it is normalized to all of the blued steel models and divide by 1000, you get .429 which is the bullet size. Everyone knows that .429 is the size of a .44 Magnum bullet so that revolver is a .44 Magnum. ... Or is it a .44 Special? Dang! Nevermind.