Perhaps an additional perspective would be to look at the two earliest known formal archery clubs in the U.S.
The first would be the United Bowmen of Philadelphia organized in 1828. They called themselves "bowmen"; however, in my archives, I don't recall any specific reference to bowhunting although some of them may have taken an occasional shot at game. They were principally target shooters. Their uniforms of the day were quite elaborate. On the other hand, they did enjoy a good time and their special punch was known to be quite potent.
The second known archery organization was the Robin-Hood Archers of Boston, MA. This club was organized October 1st of 1835 [or possibly earlier]. They considered themselves "archers". From the lithograph that I have of them -- they appear to be in uniform and shooting at targets.
So there you have it -- the two earliest known archery organizations in the U.S. -- one calling themselves "bowmen" and the other "archers". Both were primarily target shooters, which also included much pomp and ritual and enjoying a good time. No doubt there was a British influence on these early U.S. archery clubs.
I prefer to think of myself as a "toxophilite" meaning "a lover of archery or one devoted to archery". Another definition of "toxophilite" means an "expert at archery" [unfortunately this latter definition clearly doesn't apply to me].
Tox Collector