Steps to replicate:

1. Create a standard post using the regular web interface.
2. Edit and save the post using the iOS app.
3. Go back to web interface and you'll see an extra standard button.

Here is what I'm seeing.

I work for a commercial theme developer, and this appears to be affecting how some of our themes function (because we rely on the regular "standard" post format to set some options). Let me know if you need any more information.

If you modify your theme's functions.php file to add post formats (i.e. add_theme_support( 'post-formats', array( 'aside', 'gallery','link','image','quote','status','video','audio','chat' ) );) then you see two different "Standard" listings shown during edits of any post that was previously modified on iOS. Only one shows up when doing QuickEdit, but two show up when using normal Edit. This obviously indicates that something unusual is being done to the "Standard" format for the post, causing WordPress to see it as something other than a standard post.

To remove those references, just add the theme support for post formats to the end of your functions.php file and use QuickEdit on all the affected themes. Select "Standard" from the popup list (even though it is already checked) and then update. That will resolve the issue.

In the case of one site, this was a significant problem, because the organization uses "Standard" to designate a category of information, and thus it was really confusing the contributors to see it added to many of the posts. For other sites, it is only a minor visual nuisance when looking at posts.

But at least the problem is now clarified, so perhaps this can be addressed with an upcoming WordPress for iOS update.