When setting up pages on Facebook, there seems to end up 3 pages.
Pressing Like on the website does not +1 the like count on the brand page in (2) above, likewise, liking the brand page doesn't update the count shown on the like button on the website either.
The App posts updates to users profile, with a link back to the App Profile Page, although it has the same functionality as the brand page, is empty as the brand page is the one being maintained.
You can't choose a username for the app profile page, nor change its category, nor 'use' facebook as this page, nor 'check in' to a profile page, nor set any other information like address/phone number; so you wouldn't want to use the profile page as the brand page as it's missing these features.
To clarify, the Graph API contains 3 objects that essentially represent the same thing, their types are as follows:
Each of these Graph objects collects their own Likes.
How can the likes be collected under a single identity? Why can't a single Graph object/page have all the features that each type of page above has to offer..?
So, a few thoughts:
The Open Graph tries to represent the world as a collection of Objects, with Types. A Facebook Page is one type. A website is another. You might have a Facebook Page, but not a website. Or a website, but not a Facebook Page. An Application is something completely different too (although it's confusing, since they DO give Applications profile Pages...). Lots of folks with websites and applications don't use a single App.
So they do not always represent the same thing, which is why they are not the same thing.
But sometimes they do, sort of, represent the same thing (as in your case).
When this happens there are a couple tricks you can do to improve brand coherence on Facebook.
1) On your website, point the link button to your Facebook Page
<div class="fb-like" data-href="http://facebook.com/mypageurl"></div>
This way at least you have a slightly more unified Like count. You can't hide/disable Page likes, so the best you can do is try to funnel website likes to Page likes. Users will see your Page Like count on the website, and when they like your website your Page count will increase.
2) Have a link on your App profile page to your regular Facebook Page
If you are using an App to publish things, there is that small tagline at the bottom of the post that links to the app. Some folks will click on it. Just add a link to your description in the sidebar saying "Visit our page here!". If there is nothing going on with your App page except a link to your real Page, I don't think you will collect too many Likes on the App page.
(I think you could also set up a custom landing tab on your App page that redirects users to your Facebook Page if you want to get real fancy. It used to work, at least, not sure if it still does.)
EDIT: 12/9/2011 Facebook is removing App Profile pages:
http://developers.facebook.com/blog/post/611/
It's all kind of a pain, I know. Perhaps worth filing a bug about? But there is a reason why things are the way they are, I don't think you have to worry about the App page all that much, and there are some ways to mitigate the problem.
Good luck!