The magnetic field of a solenoid can be “switched on” or “switched off” at will, but the magnetic field of a magnet cannot.
The direction of the magnetic field lines of a solenoid can be altered by reversing the current direction, while the magnetic field lines of a magnet cannot be reversed because the poles of the magnet cannot be reversed (unless the polarity of the entire magnet is reversed).
The intensity of the magnetic field of a solenoid can be modified, but the same is not true for a magnet.