I disagree. The steady state current through a solenoid is limited by the DC resistance of the coil according to Ohm's law. The initial current is additionally limited by the EMF generated by the changing magnetic field as the current increases from zero to its steady state value.
A DC motor behaves differently because, once it is running, it behaves as a DC generator with the generator output voltage opposing the supply voltage, the difference between the two becoming the effective supply voltage and the current being that voltage divided by the motor's DC resistance.
If you think I'm wrong I'm happy to learn something new.