زَيْدٌ أَبُوهُ قَائِمٌ: «ـهُ» connects the father to Zayd.
زَيْدٌ أَبُو عَمْرٍو قَائِمٌ: without further context, the inner clause is about ʿAmr’s father and lacks an evident connection to Zayd.
The link need not always be an overt «ـهُ»: a concealed pronoun can serve, and some contextual constructions allow omission.