Location AreaLocation Area is one or more cells. Location Area is controlled by VLR. Each time MS changes LA it needs to inform VLR about this with Location Update Procedure.
NAS - Non-Access StratumSet of protocols (i.e. MM, GMM, SM, CC, SS, SMS) and functions for communication between Ms (or Ue) and Core Network (both CS and PS domain).
Routing AreaRouting Area is one or more cells. Routing Area is controlled by SGSN. Each time Ms changes RA it needs to inform SGSN about this with Routing Area Update procedure.
Service Area is one or more cell belonging to the same LA. It is used by RAN when location request comes from CN.