A military person has committed the crime of Desertion if he/she is AWOL, and intends to remain away from the military permanently. Desertion is a major crime in the US Military. It's punishable under Article 85 of the Uniform Code of Military Justice.
A military person who is AWOL for 30 days or more is administratively classified as a Deserter.
Also see: AWOL and Desertion