What are the differences between galvanized and stainless steel?

Galvanized steel is just steel that has been galvanized, which is to say it's surfaces have been coated with a layer of zinc which provides a substantial amount of protection from corrosion.

Stainless steel is a totally different class of material, it's steel mixed with Chromium. When exposed to the atmosphere the Chromium at the surface forms a thin protective film of chromium oxide which protects the underlying material from further oxidation. Because the Chromium is distributed throughout the steel you can cut, grind, drill, etc. stainless steel and the newly exposes surfaces will be protected just as well as the original part surfaces (there are exceptions to this, but that's another question).

In galvanized steel the zinc is only on the surface, if you cut through a galvanized part you'll expose "unprotected" steel underneath. However, one of the neat and useful features of a zinc plating is that the exposed steel won't actually start rusting until all the zinc has been oxidized. The Zinc acts as a "sacrificial anode", protecting the underlying steel by preferentially corroding first. So a galvanized steel part can be scratched, have holes drilled in it, etc. and still remain resistant to corrosion for a very considerable period of time. Thanks to this property we can build things like highway signage, bridge beams, telephone poles, basically any structure exposed to the atmosphere, out of plain steel and then galvanize it for much less cost than using stainless steel and still have long-term protection against corrosion.