What is diffrence between rusting and corrosion?

Rust refers directly to the chemical reaction of iron and water to make iron (II) oxide, where as corrosion is a more ganeral term covering the interaction between solvent (in this case water) and all metals.

So rusting is a specific form of corrosion.

Just to add to curlyben's answer, to rust, it has to be open to the air, not just in water. The oxygen dissolved in the water is only enough for it to slightly rust very slowly.