i'll note that the smaller, similar looking things on the right are not actually the same device.
the ones on the left are kinda like gears which convert high torque/low rpm into low torque/high rpm. (or low voltage/high current into high voltage/low current)
the ones on the right are kinda like flywheels which are spinning masses used to store energy. (the inductor's store energy in moving charge)
it really is only that I know what the circuit is supposed to be doing that I know which is which. that and the T1 and L1 labels on the board. indeed, there are other devices that can look similar, but are tailored for a specific use. flyback transformers, current transformer, saturable inductors, and mag-amps can also be wire would around a toroid. The one in the lower left might be a current transformer, but i'm not certain.