Is there a difference between a "sports jacket", a "sport jacket", and a "sporting jacket"? Or are these merely dialectal differences?
For instance, why do various outerwear and sportswear brands call some pieces "sports" and others "sporting" within a same collection or line?
It sounds to me like "sporting" designates only those pieces associated with recreational countryside/outdoor activities like hunting, fishing, and bird watching, and so a "sporting jacket" would be a sort of country-style, multi-pocket, mid-length waxed/waterproof coat with or without a hood.
That said, we say "sporting house" and "sporting lady" as euphemisms for "brothel" and "prostitute", and "sporting goods" has a sense of sportswear items at large to it rather than a specific range.
Unlike "sporting", I guess "sports" and "sport" might have some relation -- to a lesser or greater degree -- with cars, back in the old days when the activity of driving an automobile would imply a certain attire, composing mostly of a jacket, a cap, and a pair of gloves. From these bygone days might have originated the terms "sports" and "sport" found in "sportswear", "sports/sport car", "sports/sport coat or jacket", etc.