What is the difference between n router and g router?

They are two different protocols. Most (probably all) N routers and networks cards can also do G and probably B protocol. Anything labeled as G will only do G and in amlost all cases B.

N is faster than G (but you'd never notice the speed difference if you are just connecting to the internet, they are both way faster than a home internet connection.

N should, technically, have a bit longer range than G, but in real-life most people don't see a great deal of difference here.