Typically, it has to do with the parallax setting. A centerfire rifle scope would have the parallax set at about 100 yards (brands differ?). A shotgun scope would have the parallax set at about 50 yards. Also, there are sometimes differences in the reticles.
I have a 2.5 power on my 336 30-30 and love it but it's a bit different being a scout scope.
Leupold FX-II 2.5x20mm Ultra-Light Rifle Scope is what you might want to look at.