Recently Gmail changed their web interface, and introduced several different inbox views. I tried them, but quickly returned to the default, which shows only the number of new messages in Inbox, and ignores the other tabs.
Gmail on my phone made the switch over to showing everything, showing unread first, but the problem is it notifies for Everything.
Google claims that you can't change this from your phone, but changes made to your desktop web interface will propagate to the iphone after a few hours.
This isn't happening. 3 days now, I still get notifications for everything, and the badge on the icon shows total unread rather than inbox unread.
Stopping and restarting gmail made no difference.
Restarting my iphone made no difference.