I'm more confused why this would be used with those two words, when a jacket and a coat are basically the same thing. In fact, they're synonyms.
Generally speaking, if we are to include all possible variations, a jacket is a lighter garment that is hip-length or less, while a coat is a heavier garment that is hip-length or longer.
That and jackets can be smaller then too. Wait then it would a vest? Honestly, idk much about clothes.