I'll be interested to learn if there is any agreed upon concensus definition that should be used.
"Engagement" or "action" do not necessarily imply a scale and can encompass both I believe. "Battle" and "skirmish" do imply scale. Clearly, a battle should be more signficant than a skirmish, but by what criteria? Size of the forces available--even if not engaged? Casualties? Percent of forces actually engaged? Percent of forces on either/both sides who were K&W? Intensity or type of engagement? The objectives when weighed against intensity? (Both sides fighting for a decision rather than delay, probe or feint.)
What would pass for a battle early in 1861 would be only a skirmish later. Some skirmishes between small forces had greater casualties (total and proportionate) than other acknowledged battles of larger forces early in the war.
I doubt there is any clear metric for determining whether battle or skirmish is entirely correct as a classification for many engagements.