The conduction current is the same as displacement current when the source is:

A.C. only D.C. only Both A.C. and D.C. neither for A.C. nor for D.C.

D.C. only

t implies that, for a DC (constant ) voltage, the capacitor current is zero.  Hence, for a DC source the conduction current and displacement current (capacitor current) are not same. Whereas, by Maxwell's equation for a time varying voltage (AC voltage), both conduction and displacement currents are same.