And the first one is a Darkwood Armory "ringhilt" rapier. They make modern repro, of course. Their products are rather good, if one obviates some weight issues in a few of their models.
The one shown here is Catalog Number AVBN #58. Go
HERE for Darkwood's general catalog and
HERE for what they call the "ringhilt" rapiers.
No way one is going to find an original rapier at these prices, I'm afraid.