“Greatcoat” is a broad term for any Regency overcoat, also referred to as a “surtout” which gentlemen wore during Regency England. Greatcoats were heavy wool coat worn over the regular attire of a gentlemen which provided protection from cold and rain. Wool is remarkably warm even when wet, and would have been a welcome layer against harsh weather conditions. To protect a gentleman against inclement weather, they were long, full, as water proof as possible, and usually sported pockets.
The boxcoat had several short capes. Having a number of capes was a way of showing off one’s taste and wealth, due to the cost of the additional fabric and labor. The additional capes would also have provided extra layers of warmth. The name is attributed to the wearing of coachmen who drove the coaches from the driver’s box, which seems contradictory to me since I doubt very much coachmen were considered wealthy. Still, they would have been an essential part of a coachmen’s wardrobe since they were expected to drive out in the open during all kinds of weather. In this picture circa 1811 to the left, this coat has a cape, which means it was a Boxcoat. Notice the almost Sherlock Holmes-style of hat?
The demi-surtout, pictured to the right, was form fitting around the torso and flared a little around the legs to allow freedom of movement. This is a demi-surtout from the late Regency/early Victorian Era, circa 1825, with a fitted waist and cape. It also has a collar which could be turned to against wind or rain.
Cloaks were still in fashion in the Regency but gentlemen were more likely to wear cloaks as they traveled or as formal wear. Sometimes these came with shoulder pads. They were often lined with silk in rich colors.
So, the number and type of coat your Regency hero wears will be a signal to others how fashionable, or how wealthy (or both) he is.