As mentioned in the Arkansas chronology, a battle is a prolonged combat involving large armies. An engagement may be a general encounter between armies, or a minor encounter between smaller forces. A skirmish is a small encounter usually incidental to a larger military movement, while an action stresses the idea of active, frequently sharp, offensive and defensive movements. The term affair simply means a fight.
Reconnaissance, expedition, and scout are similar in meaning. A reconnaissance is an examination of a territory to gain information; a scout is much the same; and an expedition is a journey for a specific purpose. An operation is a complete military action or mission of some kind. A demonstration is an exhibition of force, and a siege is a continued attempt to gain possession of a place.