Is there a difference between online and local co-op?

[Carnage]

You know, in certain games characters are bound to one screen, so playing it locally, via Remote Play or Online kinda changes nothing in how the game works. However, there are other games where Online mode allows players to go separate ways and also access different menus at the same time.

So, how does this game work? Is Online exactly the same as Local, or more convenient? I'm asking because I'm trying to understand whether I would prefer to get additional copy of the game.

[Dr. Hemmel]

I believe online is the same as local.

In online, the save file that progresses is only with the host.
The characters have to stay on the same screen
When a user enters many menus the other player has to watch. There are a few menus that only show for one player, like "quick switch between 8 recent characters" and "show current quest & status". But for the main menus it's one person at a time.