Well, what you are comparing here is the magnetic induction by passing a current through a tightly wound helix of electrical wire. A solenoid is, quite simply, a number of electrical wire turns wrapped tightly around a ferromagnetic core. Current is passed through the wire, and a magnetic field is induced in the ferromagnetic core. The other part of the question concerns interrrupting the primary or secondary coils of a transformer. Transformers work by direct proportion of the number of windings from the secondary winding to the number of windings on the primary winding. It depends on your viewpoint, if you take the core out of the primary winding, you get no electromagnetic induction to be induced to the secondary coil. If you remove the core from the secondary winding, you have no conductor to relay the electromagnetic force through the windings of the secondary winding. The two would be equal, the transformer would not function as a step-up or step-down if you remove half the equation.