I'm not stuck -- I'm stating quite clearly that the two are separate things, and that what defines Starfleet as a military in organizational terms is a constant no matter how peaceful its missions may be.
Which is not a good analogy for Starfleet, since they wear uniforms and address each other by rank and follow their superiors' orders on a daily basis. They're active service members full-time, just in a (mostly) peacetime military. Militaries do a ton of stuff in peacetime, including diplomacy, engineering, scientific research and exploration, rescue work -- basically everything Starfleet does (including space exploration, since most American astronauts have been military officers). Being an armed force is fundamental to the definition of a military, but that doesn't mean that using those arms is the only mission of a military. It just means that's included among its responsibilities, to be carried out if and when it becomes necessary.