Tawaf al-Qudum is the arrival tawaf; a pilgrim may validly perform the Hajj saʿi after it. Tawaf al-Ziyarah is the obligatory Hajj tawaf after the Day of Sacrifice. Their causes and legal statuses differ.
Completion of the arrival tawaf does not remove the visitation tawaf. A valid saʿi following the arrival tawaf can, however, change whether another saʿi is needed after the visitation tawaf.