What Brokennock says is true. Without falling to far down a etymological hole, That particular punch is designed to produce one of the variations on a round braid lacing, all of which look
something like this:
note how the leather goes around the edge creating a new one.
Stitching per se is usually a straight line, not lapping over the edge, with a few exceptions like a blanket stitch (not the only one). Here is a drawing showing stitches marked and punched with a angled diamond punch.:
Not the only use of the words as you can lace up your cod, unlace or lace a ladies bodice or corset, lace you boots etc. And lace itself in most of the Muzzle loading era will refer to a particular kind of decoration on military coats, and all the lacework found on macaroni type clothing and any dress clothing before the Victorian era.
The drawings are from Ron Edwards
Bushcraft 8 Bush Leatherwork, 1984, The Rams Skull Press, Box 274 Kuranda, QLD, 4872, Austrailia
Now that I am standing up to my ears in that etymological hole, I need to pull myself out before someone fills it in,
I am Mad Michael.