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
George W. Cullum's Biographical Register of the Officers and Graduates of the U.S Military Academy at West Point, N. Y. (1868), includes more precise definitions. To his language the following phrase should be added, "If the smaller of the two forces is [unit size], then...."
With that additional condition, we can surmise the following from Cullum,
Army = battle
Corps = engagement
Division = combat
Brigade = action
Regiment = skirmish
Lesser unit = affair
Since at least two regiments and probably more were involved on the Confederate side, the fight at Bardstown on Oct. 4, 1862, comes close to qualifying as an action.