A pier & beam foundation is like that of a deck.. footers are poured (or laid if there is no frost in the area) and posts are set on top of them (or the footers extend up and act as posts.) Then, all the posts have beams laid across them & the joist structure is built on top of that.
A masonry foundation is a traditional basement - walls are built around the perimeter and joists are spanned across. (Sometimes with posts in the middle to handle long spans.)
Why do you ask? You must be in the South if you are considering pier/beam.