Here is a brief list of the parts that make up a few models of pickups.

Gibson Humbucker: Traditional

Bottom plate is used to support all the components of the pickup.
Adjustable bobbin is the screw side.
Non-adjustable bobbin is the stud side.
Bar magnet of a desired material for specific pickup model.
6 adjustable pole pieces used in the adjustable bobbin for minor string balance.
6 studs used in the non-adjustable bobbin.
Metal spacer to conduct magnetic field to adjustable pole pieces.
Cover is used for maximum shielding and bobbin protection.
Hookup wire connected to the fine magnet wire to give better connections.
Tape is used to protect the coils and secure hookup wires.
Magnet wire of various sizes for particular sound and output desired.
Shielded or 4-conductor cable that connects to the controls.
4 screws to hold bobbins secure to the bottom plate.
Wood or plastic shim to keep the bobbins level.
Gibson P-90: Commonly called a “Soapbar” pickup
6 adjustable pole pieces for minor string balance.
Bobbin that is wound as a single coil.
2 Bar magnets with like polarities facing each other.
Bottom plate to hold components secure. Can be “soapbar or dog-ear”
2 wood screws to hold magnets and bobbin secure.
Metal spacer to conduct magnetic field to adjustable pole pieces.
Hookup wire to connected to the fine magnet wire from the coil.
Tape to protect the coil and secure the hookup wires.
Plastic or metal cover to protect the fragile bobbin from abuse or wear.
Shielded hookup wire connected to a solder lug on the bottom side of pickup.