Ghadāt al-bayn combines “morning” with “separation,” locating the grief at a specific time. Yawma taḥammalū identifies that occasion more closely: the day on which the people packed and departed.
Taḥammalū is the third-person masculine plural perfect of Form V. In this context it means to load up for travel and set off, not merely to bear something in the abstract.
A prolonged period of loss is condensed into one morning and one act of departure. This precision of time strengthens the emotional scene.