An assessment cycle is used in SAP to assign all primary cost elements and secondary cost elements from a sending cost center to the receiver cost center.When you want to transfer costs from one cost center to another costs from one cost center to another through an assessment cycle, sap use a secondary cost element and accumulates all the primary cost and secondary cost and send it to the receiving cost center.

COPA Assessment cycle assesses costs from a Cost Center to COPA Value Fields. 

A distribution cycle is used in SAP to transfer primary costs from a sender cost center to receiving controlling objects. The original cost element remains the same.