With regard to CM1 they were called operations and were essentially a complete battle played out on a single map with the fighting broken up into a number of engagements (up to 10) happening over a relatively short period of time, like up to 24 hours or so, depends on how it was setup, it included the chance of night ops. So one operation might consist of six 45 minute fire fights on a largish map with the front line adjusting on the map depending on the ending positions of each side. IIRC the map state and destroyed vehicles etc were all retained over the course of the battle and you'd get some resupply and reinforcements happening during the lulls between fighting.
As I mentioned above I really don't like that this feature was dropped. To me, from what I've read, this far more along the lines of how real battles played out. With scenerioes we have now we get just the single firefights and don't have the option to simulate multiple attacks and counter attacks with fighting over an objective flaring up then dying down many times over the course of a day which happened basically all the time.