Another is affair.
The earlist military dictionary I can find for the United States is dated 1810. The determination of the severity of these terms in the military sense was by regulation. Over the years has had to be modified to be more accurate in recording individual unit histories.
From this dictionary it states....
Action- any engagement between two armies or any other smaller body of troops
Affair- any slight slight action or engagement
Battle- an action were two armies are engaged and is of two kinds, general (whole army is engaged), particular (only a part is in action.
Engagement- same as battle.
A handy dictionary of military terms, / by Major W.W. Knollys, 1873 used more or less the same terminology used in the Civil War O.R.
another
A Military Dictionary, Comprising Terms, Scientific and Otherwise, Connected With the Science of War, by by George Elliot Voyle, G. de Saint-Clair-Stevenson - 1876
States...
Affair- means any minor action or engagement. Major Knollys, in his ' Handy Dictionary of Military Terms,' describes an " affair " as more important than a skirmish and less so than a battle.
Action- an engagement or battle between opposing forces or memorable act by an officer, soldier or detachment. Artillery exercise when guns are moved with the view of attacking another object.
Battle- An action in which the forces of two contending armies are engaged for the accomplishment of some great object.
Engagement- conflict action or battle between two armies.
United States Army Regulations, 1881 states...
A battle- important engagements between independent armies in their own theatres of war, in contradistinction to conflicts in which but a small portion of the opposing forces are actually engaged--the later being called, according to their nature, "affairs," "combats", "skirmishes," etc. A battle has for its object the determination of important questions of policy or strategy; an engagement my be partial, and yet, if it tend to these ends, it is also entitled to the dignity of being termed a battle.
and this...
In 1877, LTG William T. Sherman questioned the accuracy of the Army Register lists and recommended to Secretary of War George W. McCrary that the names of the battles be omitted from new registers. The Secretary approved this recommendation, but he did not order the battles removed from the units' national colors. Instead, the Army created a board under MG Winfield S. Hancock to examine among other issues, what was a battle; what portion of a regiment had to be engaged to have the name inscribed on the color and be included in the register; and how should the Army handle the passage of honors when units were created through various Army reorganizations and consolidations. The War Department published the board's findings in 1878. The Hancock Board defined a battle as being an important engagement between two opposing independent armies that determined a question of policy or strategy. An action involving only part of the two opposing armies that had similar results was also termed a battle. The board did not, however, offer to develop its own comprehensive list of Army battles. The board also determined that two or more companies of a regiment had to be engaged in order for the battle to be inscribed on the colors. Finally, the board concluded that regiments formed from the consolidation of two or more units inherited the honors of all previous units that comprised the organization. In 1881, revised Army Regulations included the results of the Hancock Board and reaffirmed the policy of inscribing battles on national colors. OTAG, however, was not authorized to resume publishing a list of battles in the register.
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David Upton