In Civil Engineering (drainage works), What are the differences in applications between pipe culverts and box culverts?

Culverts means a covered hydraulic structure which conveyed fluid. In terms of hydraulic performance circular section is the best geometrical section. therefore , for small discharge, precast concrete pipes or ductile iron pipes are normally used which are circular in shape.

But for very large flow, precast circular may not be available in market  and fabrication of formwork is difficult thats why for very large flow, box culvert is used.