"A battle is a general action between two armies; if only a small portion of the forces are engaged, it is usually denominated a combat, an affair, a skirmish, etc., according to the character of the engagement. Battles are of three kinds: 1st. Defensive battles, or those fought in a chosen position by an army which awaits the attack of an enemy. 2d. Offensive battles, gr those made by an army which attacks the enemy drawn up in position and awaiting the attack. 3d. The mixed or unforeseen battles, which occur between two armies meeting on the march."
http://books.google.com/books?id=TPwlU_S_02YC&pg=PA516&dq=affair+skirmish+combat+action+engagement+and+battle&hl=en&ei=SbqKTdyMMYfCsAOgw4yUCg&sa=X&oi=book_result&ct=book-thumbnail&resnum=7&ved=0CEkQ6wEwBg#v=onepage&q=affair%20skirmish%20combat%20action%20engagement%20and%20battle&f=false
Biographical register of the officers and graduates of the U.S Military Academy at West Point, N. Y., ..., Volume 1 By George Washington Cullum, 1868
"the term Battle Is applied to prolonged contests of armies or large bodies, usually not less than an army corps; Combat to a lesser battle, where a division at least was engaged ; and Action, for the want of a better appellation, or as a substitute for Affair, used by some military writers, is here employed to designate a minor engagement between small bodies of one or a few regiments. In the summaries of services of graduates it will be found that those terms do not always correspond to the classification in this list, which has been more recently prepared and with fuller information than was attainable when the former were written."