Briefly, air traffic services at sea are provided by two different kinds of people:
1) 'Aircraft Controller' ratings of Leading Airman (= corporal) level on Frigates/Destroyers or Petty Officers (= Sgts) on bigger ships (amphib/carrier). They fufill largely a tactical role but also cover basic ATSOCAS roles and varients of PARs.
2) ATCO Officers, either Lt or LtCdrs on carriers giving services to multiple ac in either an APP/DIR role or PAR role. Also in Flyco monitoring deck ops in a 'tower' role.
(Chief) Petty Officers and commissioned officers both work together at Yeovil/Culdrose giving all the services out of there.
None of the above to be confused with the 'fighter controller' sub-branch. They are warfare (ship driving) officers with an adqual. Generally known for their limited abilities at providing ATC services. Not specialist air traffickers, and do not complete JATCC or anything close to it.