Alot remains to be learned about these. I can tell you it appears that in 1921, the first sets of these were issued in sheets--14 players to a sheet in two rows of 7, with pitchers and catchers on top. Each designated position looks the same for each team. Here's a partial White Sox sheet:
As you can see, unlike later years when the player info was typed or printed onto a label, my Chisox sheet has the info printed right on the base--note how the shoes on some players run onto the base. Also note how the '21s do not tell you which way the player batted, and thus there is a gap and one less line of text. Finally, unlike subsequent years, the '21s do not have the bottom number corresponding to a pre-printed base. Compare to this White Sox catcher, probably from 1923:
I believe that sometime after 1921 the company provided the sheets with numbered-only bases and then stickers/labels for each team. I don't know if they switched to this format right away in 1922 or some time later-- if later there should be sheets with the "info base" reflecting subsequent rosters. I assume if you already had a board and the die cuts you could simply order the labels for subsequent seasons, but wondered if a consumer had the option of buying the sheets with pre-printed info on it after 1922 or instead was simply stuck with the numbered bases and a bunch of labels.
The post-1921 players are found with different fonts on the labels, and some look to have been generated by a typewriter. Some of the labels appear to show a more perforated edge than others also, as maybe this aspect changed over the years as well. Later years also abbreviated the two league designations.
In watching these from time to time on ebay, I do not see that the team uniforms changed at all over the years-- a 1921 Browns player will look like a 1930 Browns player. Finally, I note that my die-cut players are cut real close--the image actually goes outside the jigsaw line on occasion, whereas the players from later seasons seem to have a little more white background surrounding the player's body. Could just be my sheet, as there is such a small sample size that I can't make assumptions, but it's something to think about--i.e. that they re-cut the players (or reduced the size of the images slightly) later in production.