Often, the instrument was a simple statement: Bearer is ________, from ___________ County, state of ____________, as attested by my seal and his mark below.
There appear to have been many variations on this theme. And when families moved, their various documents moved with them -- just as yours do today. Usually, upon settling in a new area, identity only needed to be established once.
Of course, a deed from a previous land sale or a birth certificate or marriage license would suffice. As a general rule, proof of ID only needed to be presented once. Presumably, the local law enforcement (a sheriff, e g.) would interest themselves in new arrivals and establish their bona fides.
Only strangers needed to ID themselves, of course. The process seems to have been more-or-less informal and doubtless far from perfect. But there were few "furriners" in our midst at the time, anyway.