A Scenario game is molded around a theme like the movie Eragon, you have dragon riders, wizards to cast spells, you have props like a dragon egg, bag of fairy dust, and so on. The game follows a basic story line, the red team are the bad guys trying to destroy the realm ( I'm trying not to geek out too bad! ), the blue team is trying to prtect, and so on.
A Milsim game is molded around actual military battles, D-Day ( WWII ), Blackhawk Down ( Somalia ), Saving Private Ryan ( WWII ), not so much the story line but the battle itself.
Woodsball is what Red said!