I heard there was going to be coop and drop in drop out but is there competitive play in the story or is it separate?

Same exact thing. Search before asking questions in the future.

Well, because it is drop in/out it is all competitive play, if you have that feature on.
For example in one of the interview videos they talk about how you can turn off the Drop in/out feature and play the whole thing solo, or have your friends join in and you can play together with up to 4(or 8, if with players on other team, but that is online match)
So to answer your question: it is the same until look for an online match.