With tools: Is there some defining characteristic that makes something a wrench rather than a driver?

As in pipe, socket, hex, allen, combination and impact wrenches, etc. as opposed to screwdrivers, nut drivers and impact drivers, etc.

Is it the torque plus the gripping?

Is that what defines the difference between an impact driver and an impact wrench, for example?

Is a ratcheting screwdriver, that works by ratcheting, of course, like a socket wrench, not a “screw wrench” because it has the torque but not the gripping that a socket wrench has?

If you made a nut driver with a t-handle, like an Allen wrench, would it then be a “nut wrench” instead of a “nut driver”?