Paper swatch is meant to imitate your paper color for when you are printing to colored paper. It's like "non-printing color" as in the resulting background is really transparent.
In your example image, the "white background" is just the background color of acrobat.
To make background color for your document, I'd recommend Master pages.
From the top menu:
Window > Pages In the top of this panel ( as a default ) you will have the Masters and the pages are shown at the bottom.
More instructions at the bottom
Make a new master page ( or use the
Fill the master page with Rectangle tool ( Make sure to get those bleed area's as well. )
Here's an example image where I have set blue rectangle along with red one into a master page. As you can see from the image, this repeats throughout all of my pages.
This acts as a background for the pages you set this master page into. ( You may want to think of master pages like they were locked layers that are always at the bottom and you can assign them to specific pages easily ).
You can't arrange anything below the elements in a master page,
unless you are in the master page of course.
None of the selection tools will react to the elements in master page if you're in the Page view.
Master pages are great for elements that are static, like if you have a header that repeats throughout all of the pages, this would be the way to go. The red rectangle in my example exists to show that you can put more than just a background color in there.
The bottom of my Pages panel says
1 Master and also I clearly have "A-master" selected, these two things indicate that I'm in Master page view at the moment.
A on the top of the page thumbnails in my example image indicates that I have Master page A set to all of the pages.
Switching between Page view and Master page view
You can double click the Master thumbnail and the same thing applies to the page thumbnails. You'll be shown a clear indication of selection when a specific page is selected ( single click just selects a page ).
Making a new Master page.
Drag Master page from the thumbnail into the
New page icon or Right click Master page and select
Duplicate Master page..
Setting a Master page to Pages.
You can do this simply by dragging a Master page thumbnail into a Page thumbnail.
If you want to set Master page to multiple Pages at once, select the pages you want and Right click one of them and select
Apply master to pages.
A little more about master pages