I agree with the notion of a "hand vise".
I'm sure a vise of this form has been sold under the name, "engineer's hand vise." But this basic form dates back to at least the 17th century when they were all hand forged.
As far as I know Engineers and Woodworkers have similar vices.Hand vise as opposed to bench vise.
Engineer's (metal worker's) vice as opposed to woodworker's vise.
That's how I take it to be, anyway.