I would use the term radius to describe the "dome" that is built into the top and back, also the fingerboard will have a radius built into it from High E to Low E on a steel string. I haven't built a classical guitar, but I hear that they use a flat fret board.
I would use the term depth to describe the dimension of the body, usually measured at the base of the guitar (the deepest) and the neck (the shallowest)
There are all kinds of reasons to build with a radiused top and back, and certainly one of the most important is to help allow the large expanse of wood to move in humidity fluctuations in a somewhat predictable manner. If you have to live and build in an area like I have to, this is a huge consideration. There are all kinds of other things that building with a domed top and back do, including helping to shape the tone of the instrument, strengthening the structure to list just a few.
[edited to correct wrong radius]
I use a 25' radius for tops, and 15' for backs, for no other reason than that is what I heard was the norm when I first started out and that is what I built my radius dishes at.
For an excellent tutorial on how to build a radius dish see Graham McDonald's article. Wish I had seen it before I built mine.
http://www.mcguitars.com.au/forum/viewtopic.php?t=231