Steel rusts easily, which is why it's common to modify the metal to protect against corrosion. Stainless steel and galvanised steel have both been modified, but in different ways.
Basic steel is a mixture of iron and up to 2 per cent carbon. The carbon makes the metal much harder than pure iron.
Stainless steel is a steel alloy with chromium and, usually, nickel. The chromium helps block rust from forming.
Galvanised steel is steel that has been coated with a layer of zinc to protect it from air and moisture. The zinc isn't just "painted" on--that's plating--but rather bonds on an atomic level to the underlying steel.
Stainless steel is more expensive than galvanised steel.
The corrosion protection in stainless steel goes all the way through the metal; scratch stainless steel, and there's just more stainless steel underneath. With galvanised steel, the protection is only on the surface; a gouge that penetrates the zinc layer will expose the underlying steel.