My interpretation is this: When we call someone a woodman, we are refering to a man whos main work tools are a felling axe and a fascine knife or bill hook. He is a wood cutter. A charcoal burner for instance must also be a woodman, because his trade requires him to remove wood from the forest or woodland to be used to make charcoal. Where as this person may also be a woodsman, a woodsman is not likely to choose the trade of a charcoal burner as his main job of work.
Painting of an 18th century woodman.
A charcoal burner's camp.
Forest scene with woodman and his dog by Thomas Barker.
The Woodman's return engraved by John Whessell 1760ad.
A woodsman as I see it is a person who spends a lot of his time in the forest & woods and derives part of his living if not all of it from those woods, but his main purpose is not in cutting wood to earn a living. A woodsman may have many other occupations, such as a Ranger, scout, courier, farmer, trapper, or hunter. His main tools of occupation are the Flintlock gun, the tomahawk & the hunting knife among others, or if in England he is likely to be a poacher or a gamekeeper.
Most of the paintings of woodmen are English or European, the definition in Europe or England of a woodsman would be as I said earlier, a poacher or a gamekeeper. So we are not likely to find any paintings titled "The Woodsman" and showing what we accept as a colonial woodsman.
An untitled painting by Sedgwick.
The woodsman By Gainsborough.
Titled The Woodsman but no provanence.
A modern painting of "The Woodsman" by John Buxton.