In wa-ʿalayhi al-qadaʾu, ʿalayhi acts as the fronted predicate and al-qadaʾu as the postponed subject, expressing an obligation.
In wa-la yalzamuhu qadaʾuha, la negates, yalzamu is the present verb, and qadaʾuha is its subject: making up the Umrah is not required.
Reading these formulations side by side shows when a make-up duty is imposed or denied.