In the US and Canada the clamp fastened to a workbench is a vise, but a vice is a moral flaw or bad habit. So in North America a person with an overly firm handshake has a vise-like grip. Writing of a “vice-like” grip invites racy jokes at your expense.

However “vice” is the spelling of both words in UK English, and the Oxford English Dictionary defines “vice-like” as “firmly tenacious or compressive.”