The Bitcoin market cap is usually quoted as every BTC currently in existence times the current market price. This is not true because the majority of BTC were never traded for currency. Even worse during a rally the supply dries up because people do not want to risk having the price surpass their ask significantly.
And how is this different than stocks?
You can't really compare it with stocks. Owners of a company's stocks or other securities, actually have a claim on the company's assets, some of which are always physical (larger percentage for an airline as an example, smaller percentage for a software firm, and so on). Even if stock goes to zero, there is always some recoverable value. This is why, when companies have substantial physical assets (plants, equipment, inventory, etc.) their stock cannot go to zero. Someone will buy them before that. Debt changes the variables, but even if the company defaults, some debt is recoverable.
"Market capitalization" in that context is a useful metric when compared to the actual asset base of the balance sheet, to gauge whether a stock is richly or poorly priced (and in the case of things like FB as an example, to try and justify it

).
Owning bitcoins (which is a very vague term anyway, the "owning" part I mean) does not represent a claim on anything of value. If their price ever goes to zero, we probably won't even talk about it with anyone anymore.
So, terms like "market cap" have no meaning when talking about BTC, but for a different reason, IMO, than what the OP suggested. There are many more differences between bitcoins and securities, such as what happens if the grid shuts down for a while...
And BTW, Spiff, nice to see you here :-). KAFA 4 ever ;-).