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.
General Overcoats
Greatcoats
Topcoats
The word Topcoat is often used for any overcoat that is lighter in weight; it is not useful for severe rain and storms.
Other Coats
References:
(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.
(2) https://www.ties.com/blog/mens-coat-guide
(3) https://www.lanieri.com/blog/en/how-to-choose-a-mens-coat/
(4) https://www.gentlemansgazette.com/overcoat-dos-donts/
(5) https://www.esquire.com/style/mens-fashion/g2014/best-winter-coats/
(6) https://www.saba.com.au/foley-business-coat--MW18405.html
(7) https://www.houseoffraser.co.uk/brand/all-saints/foley-coat-ym2945