I thought that the term 'clincher' was originally used to mean either sort of detachable tyre; that is to say, beaded edge or wired on. Although I think that the wired on type may have been patented earlier, it was the beaded edge type that became more popular in the early twentieth century because it is easier to fit or remove. The recess into which the bead fitted was sometimes called the clinch, I believe. Either kind of detachable tyre could be called a 'clincher' to distinguish it from a tubular. Calling a tyre 'wired on' distinguished it from beaded edge. Is 'clincher' a term of American origin. I don't recall seeing it in print in older British books or magazines. (Two nations divided by a common language again?)
Comment from better historians than me would be welcomed.
Stuart Tallack in West Sussex