re: While testing an app, why am I able to receive notifications on one device but not the other?
1. Always reboot a device that appears to not be working as it should. That will normally solve a good deal of the problems.
2. I assume that the app you're testing is on both devices? Don't be offended. You'd be surprised to find that the simplest of things are often overlooked.
3. You stated that the "application settings" are the same for both devices, however, are the "notification" settings the same in the device settings?