While the terminology is admittedly ambiguous and contentious, I don't think anyone actually uses the terms as you've described, Gavin. Indeed, the term "secondary" itself is misleading, as it is short for "secondary fermentation," and of course there is no actual fermentation occurring at that point in the process. It is merely a conditioning step, or sometimes dry hopping. Big breweries call them "Brite tanks" because it is used to allow the beer to clarify ("drop brite"), while simultaneously carbonating.
Nevertheless, if one insisted on referring to the conditioning vessel as the "secondary" vessel, it would indeed make sense to refer to any subsequent transfers in kind. i.e, the tertiary vessel, quaternary vessel, etc., regardless of the futility and pointlessness of such transfers.
In wine and cider making multiple rackings are common on the homebrew scale. This is where the terminology I mentioned is most valid, although it applies to any homebrew venture where the brewer uses multiple rackings.
On the commercial scale I completely agree, different terms for different kit. Primary to bright-tank being so common as to be almost ubiquitous.