The walking coat is a knee length coat for women meant to be worn over the trousers.
The jacket is usually a hip-length garment, while the coat can be of any length.
The opera coat is the most popular form of women's formal coat. It almost sweeps the floor and is generally made of some opulent fabric like velvet or silk.
Women's fashion has been variously inspired by the trends in the men's scenario. Thus the waist length Spencer jacket worn by men in the 18th century was adopted by women in the early 19th century.