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Al C.risafulli1938 Goudey had two different wrappers. Neither were marked as "series one" or "series two". Here are both, the differences are subtle.
My speculation is that the top one is from series two (the ones with the cartoons), because the wrapper is smaller in size and contains less graphics, so was probably slightly cheaper to produce. I think it's possible that by 1938, Goudey was starting to feel some financial pressure, and produced a second series of cards that was virtually identical to the first (same players, just added artwork, with a very slight modification to the backs).
The backs of the second series of 38 Goudeys make reference to the cards being part of a series of 312 cards (beginning with #241, with the numbering taking over at the end of the 240-card '33 set). Using Goudey's numbering system, only 288 cards were produced, as the '38 set wound up being a 48-card set. This, coupled with the absence of MANY of the day's stars (Hubbell, Simmons, Grove, Dickey, et. al.) leads me to believe that the set was initially intended to be much larger than just 24 subjects. A larger premium set in 1939, with three different types of cards and 96 different cards in total, lead me to believe that Goudey focused more on selling VOLUMES of gum, rather than just individual card packs.
...which is a very roundabout way of saying that for the second series, Goudey probably skimped wherever they could, thereby shrinking the wrapper and using less ink - so the smaller wrapper is likely from the second series.
-Al