Conduction current flows through a conductor, while displacement current appears in the region where the electric field changes with time (like between capacitor plates).

• For D.C. (Direct Current) the electric field is constant

So they are not equal.

For A.C. (Alternating Current) the electric field changes with time displacement current exists.
In a capacitor connected to an A.C. source, the displacement current between plates equals the conduction current in the wires, so that total current remains continuous.