With ordinary coordination, as in a second independent statement such as وَجَاءَ عَمْرٌو, another event or judgment is added. With جَاءَ زَيْدٌ وَهُوَ ضَاحِكٌ, the following clause tells us the manner of Zayd's arrival.
The first primarily joins judgments; the second supplies a circumstantial restriction. Merely spotting wāw is insufficient. One must examine the antecedent, clause structure and communicative aim.