The sine/cosine pots have four excitation points on the resistive surface, to be connected to balanced drives, and have truly continuous rotation of the two wipers.
Normal "continuous rotation" pots have a dead zone between the ends of the resistance element (20 deg in my example above).
The only other way that could work would be to have the "endpoints" diametrically opposed (180 deg apart) to allow continuous rotation with no dead zone.
"Helipots" (trademark) use a helical winding, which can have 3, 10, 20, 40, or so turns from end to end.
Years ago, when analog servos were more common, surplus houses had stock of "servo" pots that used a gland mount (with screws) instead of a bushing mount (with nut).