As far as I know Fully riggid sails are called wingsails while long cord masts (often with a much flatter profile) are called wingmasts. In literature wingmasts with soft sails behind it are often refered to as so and so % wingmasts. For example a soft sail rig with a wingmast that has a cord of 30 % of the overall average cord of the compet rig is refered to as a 30 % wingmast rig.

Of course wingsails come in different shapes. You can have a wing out of one section or have a wingsail that is made up from several vertical section that are spaced a little apart. These wingsail are often described by the number of slots that are between the segments. A two part wingsail is than refered to as a single slotted wingsail. Three part wingsail as as a double slotted wingsail and so on.

In the case of miss nylex which had three segments but where the rear panel was split into two (almost) vertical alligned flaps the wigsail is still refered to as a single slotted wingsail despite the fact that it was made up out of three segments. The reason for it is that from a aerodynamic point of view it behaves as a single slotted wingsail.

Hope this helps although I'm often told that I don't know my rear end from sailing technology. So I could be completely of the mark here.

Wouter