You can use the same database for both forum sites. I've done this already. You just use the same connection string.
As for files such as avatars, etc, those will be stored in the file structure of whichever domain they were uploaded from.
If User3 uploads GIF1 to DomainA, it won't be shown on DomainB because it's not in the same directory on the server. If you store image files ON the database, then you can have two forums with the same content, same users, but you can use two completely different theme designs.