A cabochon is a stone cut with a domed top and (generally) a flat
bottom. I believe that the term derives from the french "caboch"
meaning a man's bald head. With cabachons. the goal in cutting is
normally to avoid having any flat spots, whereas flat spots are
pretty much the core concept in faceting.
The term "vermeil" in current usage is fancy talk for gold plating
over silver, applied by any means. The term vermeil derives from the
French term for the pigment vermillion, which was a mercury
compound. The old way of making vermeil involved use of a mercury
amalgam, hence the connection with vermillion.