ConstructionLinkCircumstantial meaning
جَاءَ زَيْدٌ رَاكِبًاSingle accusative ḥāl; no wāwState of Zayd during arrival
جَاءَ زَيْدٌ وَهُوَ ضَاحِكٌWāw plus pronounZayd arrives while laughing
جَاءَ زَيْدٌ وَعَمْرٌو يَتَكَلَّمُWāw without a pronoun of ZaydContemporaneous speech as background
All three can express attendant circumstances, but the way the link is marked differs because a single-word ḥāl and a clausal ḥāl have different structural needs.