As far as I know, aviation in both divisions are almost the same. They fly various aircrafts, they do dogfights, air to ground attacks, air transports, electronic attacks, and more. Can you say that Air Force and Navy pilots are different in some ways?
Navel aviation pilots are specifically trained for anti ship and anti submarine warfare roles and they are also trained for carrier based operations. They are also trained for ground attack, dogfight etc. Air Force pilots does not have carrier based landing skills and they do not have anti submarine warfare capabilities.