When I started collecting, chips with the Paulson top hat and hooked-cane were all called "hat and cane". Then some collectors started looking closer and noted that some of the hats had very shiny surfaces, and the canes seemed to be a little longer and thinner. We called them Christy and Jones mold, as the collectors in those days (early 90's) seemed to think that was the way to distinguish older chips before Christy and Jones had a breakup.

I can still remember Perloski's posts that pointed out that not every chip with long canes had shiny hats, so we shouldn't call them all Christy and Jones chips. I argued with him for a couple of weeks, but he was right of course. Someone suggested just calling them the Long Cane Variety on one of the bulletin boards, and it stuck.

You're right that those designations aren't strictly precise, but to us older collectors, they match our memories. The nomenclature also matches the symbols that The Chip Rack authors squeezed into the narrow column in their reference book as they only had a few characters to work with.