أَزَيْدٌ حَاضِرٌ أَمْ عَمْرٌو؟
Is it Zayd who is present, or ʿAmr?
Here connected am introduces two alternatives for one identification; the answer selects one person.
أَزَيْدٌ حَاضِرٌ؟ أَمْ عَمْرٌو غَائِبٌ؟
Is Zayd present? Or rather, is ʿAmr absent?
When the speaker turns away from one question toward a new one, am may be disconnected, containing the force of “rather” plus a fresh question.
The distinction changes the answer sought. Connected am supplies alternatives under one issue; disconnected am introduces a shift in discourse.