In the story modus (offline) you play as ethan and follows his adventure.
So it has/is a proper story, unlike PSO.
The extra modus is bacially the stages you unlocked in the story mode,
but you can play them with your custom character.
It doesn't have a storyline nor npc lurking arround in the cities.
There is nothing more to do than trying to get s ranks in each mission.
As for online modus, it takes place after the ethan's adventure
Honestly they should have done it like in homeland(GCN),
enable network(online) modus only after finishing the story mode first.
Who knows maybe it will be in the oversea versions ^^