Service is an event in which an individual takes the responsibility that something desirable happens on behalf of someone else. It is also a state of being subordinated to an individual or a group.
"Lancelot was in the service of King Arthur till his death."
Serve means to be a formal servant for someone greater, to worship in official capacity. It is to be a servant or work as an aid to someone.
"He went to serve his country for a year by joining the military."