@W. Hilditch, nice looking end-grain block you've got your pieces sitting on. Nice pieces, too...
This is an interesting thought question. Yes, sets are typically marketed (at least these days, don't know about historically) as a count of the number of separate pieces in the set, regardless of their function. Like in a set of something with a holder, the holder counts, too.
But, marketing aside, how do we count them?
Personally, I define it like this - if the pieces are only designed to be used together, they have no individual function (unless you get very creative), then the set is one piece of cookware.
But if each individual piece can be used standalone or in conjunction with pieces other than what they came with, then they are single pieces.
For example, a waffle iron, can you really use the individual pieces separately, without getting really improvisational? And a syrup warmer, do the lid and trivet really serve any meaningful purpose without the pitcher? I would call each set a single "piece".
While a lid, though there's no "standard usage" for a lid without a pot or pan to put it on, a single lid can service multiple pots and pans of the correct size, so I'd call that a separate piece.
Just my opinion.