Qual é a diferença entre military e army e troops ?Podes indicar apenas respostas exemplo.

"Military" is the most general, and refers to any of a nation's armed forces, be it army, navy, air force, etc. In most nations it does not include police, which are considered a civilian force, completely separate from the military.
An army is a nations ground forces, military who use their feet and land vehicles to move about. If a nation still has a cavalry, it is traditionally considered part of the army as well. In the USA, the Marines are separate from the Army, because their primary nature is "amphibious", moving about on land, rivers, and small bodies of water.
"Troops" are an armed group, usually made up of army men, but could be other forces as well.
The USA also has the Coast Guard, normally not part of the military. It is a water-based group whose functions are water rescue, light house management, and policing (intercepting boat traffic for drugs and other smuggled goods). In time of war, however, the President can "militarize" the Coast Guard, moving them to the Department of Defense from their normal Department of Transportation position.
Note that even though the USA has the Air Force, the other parts of the military (and Coast Guard) also have planes, jets, and helicopters. These are to provide tactical support to the primary role of each part of the military. The Air Force focuses on strategic air power, such as bombers, missiles, attack drones, etc. There is overlap, such as the Naval Air Force has bombers which work from aircraft carriers and ballistic missiles which work from submarines.