What's the difference between lined and unlined brake cables? What style is appropriate for Campagnolo 1980s vintage equipment?

lined has a thin tube of a slippery plastic (like Teflon) inside of the wire coil, so the cable slides against that and not against metal ridges. IMHO it's always appropriate when you want less friction and better performance, including any year of Campy equipment. I've even added the liner to old vintage housing to make the braking better, you don't see it so no Concors d'Elegance points are lost

IIRC, that cable came on the scene about 1970-72. Unless your bike pre-dates that, it is appropriate, probably even for a Concors.

The one's you wanted in the early 1980's had a Teflon liner. And the cables you wanted were the multi-strand round-wound Teflon-coated cables. You said that, and the worker would vanish and return with the goods. I don't know what Campagnolo was selling, but we'd already figured out they were ridiculous for somethings. Like their over-priced tool-sets.