Steve,

That's just the sort of question that I personally find interesting, too.

To be somewhat pedantic: I don't think there were too many things ~like~ "Cheer'ly Man." I would argue that it was almost in a class of its own. I think it was a rather innovative English/Anglo-American song, and that, as a shipboard work-song, it may have helped paved the way / set the ground (choose your metaphor) for the adoption of "chanties" on ships. (Embedded in that statement is my own belief that "chanties" as a genre did not originate on sailing vessels.) A "theory" of mine is that "Cheer'ly Man" was rather exclusively "attached" to its work task - that is, it was the primary, "go to" song used when singing was in order during those (hauling) tasks, rather than one incidental example of many songs of a particular type.

Anyway: Giving it a quick scan, most of the accounts of "Cheer'ly Man" in that early period (by no means limited to British accounts) call it a "song."

There are some other terms for various shipboard vocalizations, but it gets complicated. For example, it appears that French sailors did indeed use the word "chant" at one point in the 18th c.

The related interesting question is how/why did sailors eventually - or at least *some* sailors (because there is also the very nit-picky question of whether writers give a skewed perception) - start calling the work-songs "chanty". Even though I personally distinguish "Cheer'ly Man" as something belonging to a different category than what I would label a "chanty," there is much that I *would* label "chanty" that, nonetheless, is only described as "song" until late 1860s.

I believe that the lingo of "chanty" was borrowed from stevedores, and I think (I have evidence to support this somewhere, but it's too complicated to work out right now!) that the term "chantyman" had greater currency before "chanty." That is, the idea of a working song at sea was not new, though the concept of a masterful song-leader, in the style of Black American work gangs who retained such a specialist, was more novel. And so, the term "chantyman" became familiar to sailors as the person in those role in stevedore gangs, although at first what the chantyman and his crew sang were simply "songs."   

On a gratuitous side note: My feeling - enhanced by the times I have visited those places - is that New Orleans and Mobile (previously French part of Alabama) were such unique and amazing places that most people that have thought about chanties perhaps do not fully appreciate. I certainly have trouble doing so, beyond a vague "sense." When one stands in "Congo Square" - that unique meeting place that some people credit to the birth of all sorts of influential African-American musical forms - or when one walks around the French Quarter, with its buildings that feel (to me) like one could be on an island in the Caribbean... it's its own little world. The uniqueness and complexity of this world is easily overlooked when one tackles the broad concepts of "chanties" and "sailors" and "ships" etc. in the way that "we" have tended to do so, based on the various associations we've inherited having to do with those concepts.