I am not sure what counts as the "second print", exactly but I noticed that my original release NTSC U/C version of the game (with a metallic sheen) came with a color booklet, the cover of which had standing from left to right in an arc: Riku, Kairi, Sora, Donald and Goofy. The disk itself was opaque with colored art of Sora, Donald and Goofy standing on it in the same poses as on the booklet.
My friend who only managed to snag a "greatest hits" version for U/C only got a black and white colored booklet (and the cover was black and white as well) but I can't recall what the CD looked like. So that version at least is markedly different in those two ways.
My NTSC/J copy also has a color booklet, but the booklet art is the same as the cover art. The disk itself while the same art as the U/C version is silver and shiny without color and more zoomed in on their faces.
I picked up a PAL version a lot later and this one appears to be the not the initial release version because it doesn't have a metallic sheen to the picture. It also comes with a color booklet with the same cover art, but the disk art is unique. It's opaque with only Sora in color, holding the Keyblade over his shoulder instead of with both his hands on the hilt with the blade pressed into the ground. Donald and Goofy are missing.
That is all I have in terms of the original game, excluding my final mix copies. So, while I can't say for sure if the disk art or booklet art changed between prints in the same country, I can say at least that different versions have different art between regions.