Campaign; Battle; Engagement; Conflict; Affair; Skirmish; . . . then about eight or nine more after these with "Encounter" being close to the bottom.
As I understood it, a battle had more than 10,000 men and more than 2 generals; Cooper called the event an "Affair" which would perhaps indicate one general and one colonel (as he thought he was fighting Col Phillips and didn't know that Blunt was there).
At this point in time I'm more than a little "sketchy" about the definitions since it's been so many years since I read the chart. I'll try to find it again.