S&P publish a mid-cap index: the S&P400. It doesn't overlap the S&P500[1]. You have to have a generous definition of mid-cap to describe even the smallest S&P500 component as mid-cap. The 500th component has a market cap of ~$6B.
Regardless, they're all US stocks; the comment I was responding to claimed they were not.
First the S&P 500 captures 80% of the entire US market, 80%! [0]
Second, 6B is well within the middle of the Mid-cap range for at least one common definition: "Mid-cap (or mid-capitalization) is the term that is used to designate companies with a market cap (capitalization)—or market value—between $2 and $10 billion. " [1]
Now some people might define mid-cap differently(and S&P tries to), but that doesn't change the math. If 80% of the US market is the S&P 500, then by definition some mid-cap has to be in there, or one has a very distorted view of what the middle means.
US public companies are giant these days. Of course there are mid-cap only indexes(and funds), that has nothing to do with the S&P 500 though.
As for all US stocks, it definitely depends on how one defines a US stock. S&P obviously has their definition, and it may or may not agree with your personal definition, but I generally agree that the S&P 500 is basically US companies.