Solenoid is long coil containing large number of turns. When electric current is passed through the coil, solenoid acts as an electromagnet. These are used for movement of the material.
Electromagnets are usually in the form of solenoid containing iron core. The core being ferromagnetic in nature makes it more stronger electromagnet in comparison to simple solenoid.
Therefore, loosely we can say that the difference in two things is presence of iron core.