Properly, 700C doesn't exist.
It should be 700x28C or similar.
The 700 is the overall diameter of wheel plus tyre in mm. The 28 is tyre width, and the letter is a code for the rim width, with C being by far the most common for road bikes.
I'm pretty sure that's wrong. Not 100% sure because "700C" is such a rubbish term there's no authoritative reference. I just know this from reading various (possibly wrong) websites over the years. There is a consensus.
The C refers to the tyre size, not rim width. Rim width is always sensibly given in mm.
A "C" tyre would therefore be 39mm (2x39 + 622 = 700). If you fitted one of those, if they existed, which they don't, to a 622mm rim you'd get a diameter of 700mm. Which tells us that most road bikes that are advertised as having "700C" wheels don't actually have clearance for a 700mm diameter wheel at all.
A 622mm rim with a 28mm tyre would have a diameter of 678mm if tyre sizes were reliable, which they aren't.
So the 700 in 700C is completely meaningless. Why not just give the bead diameter of 622?