(This image can be right-clicked and opened in another window if you want to see it larger.)
The first set was issued in 1939 by Gum, Inc. The "plain white border" look was one that would be revisited several times in the future by the company (after they changed their name to the Bowman Gum Co.). In 1948, that company would issue smaller-sized cards with the same design that was used nine years before it. In 1950, the design was given color, and in 1953 they released sets that had both color and black-and-white pictures.
The Play Ball design was given an elaborate makeover for 1940. While the pictures remained black-and-white, a banner and several baseball-related elements were added to "frame" the photo, with many players given a nickname in quotations. In 1941 the banner was still there, but the bat, glove and catcher's mask were gone. However, color was added to the card, sometimes emphasizing shadows as shown in the example above.
Ironically, the back designs didn't change all that much from year to year.