What's the difference between this and the white one that's $38.75?

The difference is the cable stock -- the white is a 10 AWG US-made cable, two conductors; this one is a Japanese-made "Star Quad" 14 AWG cable -- four conductors, which are paired in a star quad configuration for an effective AWG of 11. Some people like the star quad because that configuration results in more cancellation of the electromagnetic field around the cable -- hence, if you have a problem where the high-current signals in the speaker cable are inducing noise in nearby line-level cables, it'll perform a bit better on that measure. If that's not an issue in your system, we recommend the conventional two-conductor design as in the 10 AWG white cable that we sell.

Why is your premium LC-1 cable stock not available with these banana plugs? Some of us need bananas and want that cable.

LC-1 isn't suitable for use as speaker cable -- it's designed for use as a line-level interconnect. The center conductor is 25 AWG -- very skinny for speaker, but absolutely fine for a high-impedance, line-level circuit -- and if separated from the dielectric, is relatively easy to damage by flexing (being housed in a coaxial dielectric/shield/jacket combo protects it from sharp bends).

Are these 14 gauge or 16 gauge ?

The individual conductors are 14 gauge. However, since they are connected in a star-quad configuration, with two conductors on each side, the effective AWG is 11.

Can the locking banana plugs be used with speakers that have regular (non-locking?) banana plug inputs?

Yes. There's nothing special required in the binding post side -- these fit ordinary speaker binding posts, made for non-locking plugs; they just allow you to tighten the bananas to them more firmly. Kurt BJC