Gordon 
When you activate the big red crystal at the hub, at the bottom you can click on World Settings. Then you should see the menu above, survival is part of the dlc I believe.
Campaign is the main story. Adventure is a very self contained, semi randomised jaunt through your chosen environment which ends at the final boss for that area, at which point you begin again. Survival is the usual hardcore mode.
Adventure and survival don’t affect story progress in campaign but you can play with the same character, level it up and get lots of gear to take back into the story. Keep in mind that the next new level you walk into will be adjusted to your current gear score.
Under campaign you can see the button “reroll campaign”. This button allows you to keep your character and gear but start the campaign again. This might be your best bet if you don’t want to create a new toon 😉
