Both AC and DC contactors work on the principle of electromagnetic attraction. However, there are minor constructional differences between them. AC contactors have a shading coil which is a metallic ring with high remanence which provides magnetism during the zero crossing of the AC voltage.
DC contactors do not have this shading coil. Hence, if DC coils are powered with an AC voltage, the contactor can chatter as the magnetism becomes zero during the zero crossing of the AC voltage. Chattering produces an audible noise and can cause the contacts to change state causing interruption in the circuit.
AC contactors can be used with DC voltage, in theory. However, the presence of the shading coil in AC contactors can result in a higher drop-off voltage which can cause delay in contact operation.