Ref.: Lithographs displayed at Borgo San Jacopo in Firenze.
Overcoats are classified by their purpose, design, weight of the fabric and histroy/heritage.
The Three Subgroups of Overcoats
(a) The Overcoat in general: see above.
(b) The Topcoat: a lighter weight overcoat.
(c) The Greatcoat: A long and heavy overcoat with a military origin, worn originally over the uniform. A lighter and rainproof version of a military coat is the Trench Coat.
The word Topcoat is often used for any overcoat that is lighter in weight; it is not useful for severe rain and storms.
(1) The Urbandaddy Manliness website published a good summary about overcoats online. It is also found here: https://www.artofmanliness.com/articles/mans-guide-overcoats/ accessed 30th April 2019.