I have both. You are right about the pictures here making them look very similar, but they are actually different. The Sport version looks like this and also comes in a 9-inch and 3-inch inseam. Compare that to these pictures of the standard version compared to OP's link. The regular Give-and-go have a bit sturdier mesh and a looser fit as far as boxer briefs go. The sport version is thinner, smoother, more elastic with a tighter fit, higher crotch and slightly longer inseam (6-inch version).
I have no idea if Exofficio has updated the product, or if the pictures in OP's link just look different. I've never seen that many colors and pattern options before, so its entirely possible, but I have no idea as I haven't purchased any in a while.