The French are picky when it comes to clothes.
Un manteau is a coat (or overcoat).
A jacket is "une veste" or "un blouson" (+ "un caban" or "une doudoune" or "un anorak"...)
The difference is the length: "une veste (+ others listed above) gets down at mid-thighs maximum.
A coat goes down from mid-thigh to ankles.