what is the difference between inductor and a transformer...or a solenoid and a transformer
This question could be answered with a million pages if you want to follow it down the rabbit hole..
But basically here is what's up:
An inductor is a two terminal device that stores energy in a magnetic field. (Pass a current through it, it sustains a magnetic field. If the current signal is time varying then so is the field).
A solenoid (basically an electrically controlled switch) just uses an inductors magnetic field to close a switch. An example of a solenoid is in an electric starter for a vehicle with a large engine (marine application). You energize an inductor with a low voltage circuit, then the magnetic field closes a switch in a circuit which carries a much higher current to turn the motor.
A transformer is just two inductors which are placed close to one another. Only one of the inductors receives a signal. If this signal is time-varying, then the other inductor will exist within a time varying magnetic field. Faradays law says that a voltage will be developed aross the secondary coil at a voltage which may differ from the voltage applied to the first inductor (depends on the number of windings / ratio).
To summarize, inductor is a device that stores energy in a magnetic field. Alone it has many uses.
Solenoid uses an inductor to close/open a switch when energized.
Transformer uses two inductors to change voltage/current levels
Separate names with a comma.