Doing ok Chuck. I check in here frequently though don't duck hunt much anymore. Been wintering on the Texas coast for a few years now.
Here is a real basic rundown that might clarify.
Your questions are basically 2 parts. The 1st relates to the unstrung vs braced form. Between a longbow (currently referred to as an ASL - American semi longbow) and a recurve there are; a mild R/D (reflex/deflex) that has mild recurved limbs and braces to a "D" shape, and an aggressive R/D that braces with more curvature to the limbs (my preference). In addition, there are variations to recurve designs that can be much more extreme. Much of these classification differences have occured IMHO due to competition and 'perceived ' benefits of one over the other.
Most bows being made nowadays fall into one of 2 categories, either laminated using laminations of bamboo, maple, osage, etc. with decorative veneers of exotic woods and glass or carbon on the exterior OR self bows using staves of osage, hickory, locast, etc. that may or may not be backed with sinew, rawhide, etc.
Laminated bows will require a form, oven to cure epoxy, etc. while self bows require a draw knife and rasp. Flat bows aren't nearly as common as other designs but you are correct that they can be board bows. Self bows can be made into ASL, D/R, Recurve designs through heat bending.
I encourage you to search out the many 3D shoots in Michigan, especially one called the Compton Rendezvous at Berien Springs, Mi on Fathers day weekend every year as well as the Michigan Longbow Assoc.
