Do you call Naval personnel, Seaman or a Sailors? Is there another term?

Yes airmen is correct as well as seamen they are both part of the ranking system in the military both being of low rank the equivalent of a pv1-pv3 in the army

A sailor, mariner, or seaman is a person who navigates water-borne vessels or assists in their operation, maintenance, or service. The term can apply to professional mariners, military personnel, and recreational sailors as well as a plethora of other uses. Etymologically, the name preserves the memory of the time when ships were commonly powered by sails, but it applies to the personnel of all vessels, whatever their mode of locomotion.

Professional mariners hold a variety of professions and ranks which are fairly standard, with the exception of slight naming differences around the world. Common categories by department include the Deck department, the Engineering department, and the Steward's department. Mariners can also be categorized by status as senior licensed mariners or unlicensed mariners.

more.........

http://www.answers.com/topic/sailor

Both are correct.