The difference is that a military campaign concerns itself with the formal armed forces of a specific state, and as such character autonomy is constrained. The players do not have control over where they go or what their objectives are when they get there, which makes this a fine option for those players who are not the active sort who prefer to set their own goals or pursue their own ambitions; a military structure is excellent for the passive player who shows up with an attitude of "entertain me". The range of character options are likewise constrained, as the players' characters are all members of the same unit and therefore are going to be variations on a niche instead of a broad range of options cooperating as part of an umbrella organization.
In practice, a military campaign will have these features:
- You are soldiers in an army akin to that of a real-world, First World army: By default that means playing a Coalition, Free Quebec, or New German Republic soldier. Your man is indoctrinated into that state's dogma, trained in their doctrine, forced to specialize into a narrow set of applicable skills, and organized into an equally specialized unit with a specific function to fulfill as part of a larger military operation that your man likely cannot perceive as the flag officers in command can. Your man is part of a hierarchy, with one character in command over the rest of the players' characters, and the range of playable activities is as narrow as your man's area of competency.
- You are playing in a procedural campaign: The sort of unit your man is part of dictates the sort of gameplay activities that you have. Contrary to one infamous example, fighter pilots don't do ground-pounding line infantry actions. Tankers don't do hotshot mechajock action. Line infantry aren't involved in fleet battles unless and until (a) they are marines and (b) boarding actions are a thing- neither of which are common at all. By choosing what sort of military unit you want to play, you also choose what kind of game structure you want to explore. Choose carefully.
- Your campaign is married to the political and economic conflicts of the state: Military forces are used to further a state's political and economic interests. That means that your unit can be, and if applicable will be, deployed to advance or defend those interests. Campaigns that fail this fundamental reality of what militaries are for are also campaigns that fall apart because the bullshit cannot be ignored.