They are not mutually exclusive terms when used conditionally.
The military has to be subservient to the elected government when it comes to decision making on policies related to conflict, deployments etc. In fact, in many ways the Military should ideally have less functional autonomy than local law enforcement. That said, autonomy (from the elected government) in decision making related to the nitty-gritty of training, fighting doctrine, promotions (except for the top 2 or 3), equipment evaluation and recommendations etc is necessary for the military to remain a strong and depoliticized institution. We need autonomy and de-politicization of this kind in local law enforcement as well.