Well..................a lot of times folks call a Model 17 a K-22, just like a lot of times folds call an M&P a Model 10. And they are usually technically wrong.
The simple answer is that the K-22 was introduced in 1931. It was a 22 caliber target revolver built on the K frame, hence the name. They were popular with outdoorsmen, and they made ideal police training guns because of the light recoil and inexpensive ammunition. In 1957 S&W changed over to a model number system. Prior to that time various revolvers had names such as Military and Police, or 44 Hand Ejector, or K-22, K-32, K-38, etc. In 1957 changing completely over to model numbers, the K-22 became the Model 17. Dash numbers indicate different engineering changes that took place over time. Also, when they changed over to the model number system Smith began stamping model numbers on the frame under the cylinder crane. Prior to that time most Smiths did not have any kind of identifier on them as to what model they were.
Now, to get more detailed, the first K-22s were called the K-22 Outdoorsman. (K-22 First Model). Here is an excellent example. This one was made in 1935. Notice the tapered 6" barrel without a rib on top. Notice the tiny adjustment screws in the rear sight. Notice the grips, these are called Service Grips, they do not cover the frame up to the 'knuckle' on top of the grip. This revolver also has the old 'Long Throw' hammer. And of course, it is a five screw revolver, four screws holding the side plate on and one screw in front of the trigger guard for the spring and plunger that operate the cylinder stop.
You can refer to the photos I posted earlier showing the top of the rear sight and the front sight on my other K-22. Notice that the rear sight and top strap are rounded in profile, with the sight blending smoothly into the top strap.
For a short time, starting in 1940 and ending in 1941, Smith and Wesson introduced the K-22 Masterpiece. (K-22 2nd Model). The chief differences were the modern Micrometer click type rear sight was introduced, and the the hammer was changed to the short action type. The K-22 2nd Model retained the tapered 6" barrel of the 1st Model.
After WWII S&W reintroduced the K-22, but collectors refer to this one as the K-22 3rd Model. Also known as the Pre-Model 17. Note: according to collectors, only the post war K-22s are called the Pre-Model 17. This holds true with the M&P Pre-Model 10 too. The main difference from the previous models was a barrel rib was introduced. Early 3rd Models had a slightly tapered barrel, later versions had a straight barrel with no taper. Inside the new hammer block was employed. In 1955, the upper side plate screw was deleted, making the gun a 'four screw'.
In 1949 Smith & Wesson introduced a 4" barreled version of the K-22, calling it the K-22 Combat Masterpiece. This was the precursor to the Model 18.
In 1957, the Model 17 appeared. Quite similar to the post war K-22. Six inch barrel was standard, blue finish was standard, Magna grips with S&W medallions, 1/8" or 1/10" Patridge front sight and the Micrometer click adjustable rear sight. A couple of widths of hammer were available and a couple of different trigger styles.
Here are two views of my 1975 era Model 17-3. Notice the different rear sight, straight barrel with rib, Magna grips, Three Screw frame (one hidden under the grips and the screw in front of the trigger guard is gone), and short throw hammer.
Here is a list of Engineering Changes for the Model 17.
1957: stamping of the SN on the frame
1958: Introduce 8 3/8" barrel
17-1 (1959) Change extractor rod, right to left hand thread
17-2 (1961) Delete trigger guard screw, change cylinder stop
17-3 (1967) Relocation of rear sight leaf screw
1968: Delete diamond grips
17-4 (1977) Move gas ring from yoke to cylinder
1982 Eliminate pinned barrel
1986 Introduce 4" heavy barrel with serrated ramp on ramp base in place of the Model 18
17-5 (1988) New yoke retention system/radius stud package
1989: Model discontinued for Model 17-6 full lug version
17-6 (1990) Full lug barrel with new yoke retention system
1993: Discontinue 8 3/8" barrel
17-7 (1994) Drill and tap frame, change rear sight leaf, change extractor
1996 Model 17-7 discontinued for introduction of 10 shot alloy cylinder version
Note: a lot of these changes were carried across the board on many models, not just restricted to the Model 17
P.S. This is what my Model 17-3 looks like on the inside. You can see the modern hammer block is in position.
And here is an exploded view of all the parts.