Carry and possess are potentially the same in meaning. What it if it was on loan, or simply "found"? If you work at a Liquor store, and there's a gun within your control, under the counter, you could be said to be in possession.
As for "carry" - facts matter - like the relevant State law. Recent SCOTUS rulings on 2nd Amendment rights, will properly be understood to apply to all in the US, equally, under the 14th Amendment. If you can carry, legally, so can someone who isn't documented.