Military service was a period of service in a specific service branch of an armed forces.
Colonel Balthazar Edison was an Human soldier, whose military service came to an end following the formation of the Federation, when after the disbandment of MACO, he was transitioned into Starfleet, which was not a military agency. This greatly affected how he perceived the Federation for the next century. (Star Trek Beyond)
Years after his service in the Cardassian military, Aamin Marritza admitted to Major Kira Nerys that, he "would have preferred to avoid military service altogether, but I had the good fortune to be posted to the records office at Gallitep, and I turned out to be an exemplary file clerk." He further added that, "In fourteen units of service, I never misplaced or lost a record," for which, he "received numerous commendations," including the Proficient Service Medallion. (DS9: "Duet")
During war time on Talax, the punishment for refusing military service was death. Neelix potentially faced this crime at the time Rinax was destroyed. (VOY: "Jetrel")