I'm fairly new to this but if I use my common sense, a skirmish with objectives would just be.. a normal skirmish, with objectives such as taking a tower or capturing an item. Short game, sunday, sunny afternoon
A milsim on the other hand would put the emphasis on small group tactics, like in the real military and a more elaborated scenario that share similarities to such things as what a soldier would encounter in real life operations during wartime. Long game, a harsh and cold saturday morning
"Meine Ehre heißt Treue"