Looks to me like Allan's post on page 2 of the Whitcraft thread was a decent question of when is a fly so different from another that it deserves the adjective variant rather an entirely new name. Post 22 of that thread is basically what he says above. As for the question of what is variant and what's a new fly, I can't help.
My view is the noun Variant should only be used for a Flick-style tie (ie. an Adams Variant). The adjective "variant" should reflect a minor change. I'd even go far as to suggest the use of the variation (ie. I caught him with a size 16 Adams biot-bodied variant).
Anyway, that my undeveloped thought at this moment.