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davidcyclebackGelatin silver photos, which was the standard black and white photo of the time, has the front covered in gelatin. I'm assuming the front surface you describe on the Chick photo is the gelatin. The back would have a different texture as it has no gelatin. The gelatin was used to hold the photochemicals to the paper, and was only applied on the front surface where the photographic image would appear. All of Burke's photos were gelatin silver.
The gelatin coating is usually glossy/smooth, but can be in different textures like matte and linen. The texture is a style thing, what artistic effect/feel the photographer wanted.
I owned one of Dan's calendars (different team) and the image may indeed have had an extra, heavy coating over the top. I owned the calendar a number of years ago, but recall the photo being extra thick and having an unusual yellow tone, as if it was covered in something extra. The manufacturer may have been trying for an interesting visual effect on what was, after all, a collectible souvenir.