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 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.