When you export using the tool, it does additional steps to package your APK. This includes running Proguard, Zipalign, and signing your app with your own key.
None of these optimization steps are performed on the APK in the bin directory, but if you don't care about this, you can use that one for testing.
You will need to sign your app with your own private key in order to publish it to the Play Market - and make sure to never lose the key, as you need to use the same one every-time you publish.