A coat is a piece of clothing with sleeves that you wear over the rest of your clothes when you go outside. Coats are usually quite long, often reaching down to your knees or below your knees.
1. Gertrude was wearing, under her coat, a brown light jersey dress.
A jacket is a piece of clothing like a short coat. Usually jackets reach down to your hips or waist. You can wear a jacket indoors or outdoors, and you can wear a coat over it.
2. He began to undress, hanging his jacket neatly on the back of a chair.