Warren in Lancaster, PA
You can't just get another screw of the same nominal diameter and pitch and expect it to work with your nut. Different makers will have slightly different clearance and thread shape. So I would think you need both a screw and a nut. Or possibly a screw from the same manufacturer.

If I have an antique screw that is too damaged to repair, I usually carve a new one to fit the nut. I have done this many times over 45 years; let me know if you want some notes.

Paul Peters, Acer Ferrous Toolworks, makes custom screws. He is usually markets on the Red Rose Reproductions site, but I have his card with a phone number and email. His bench screws are exceptionally fine and are cheaper than Lake Erie.