HUBMOTORS
The motors referred to here are direct current (dc ) motors.

As time permits I will put up a section here showing the basic differences between brushed and brushless and geared and non-geared dc motors commonly used in hub motors. For now I've just put some commonly used terms down which describe various parts of hubmotors, these definitions are my own and may not be 100% accurate.

Terms:
hub: central portion of bicycle wheel which spokes attach too .
geared motor: a motor inside the bicycle hub which is separated from the bicycle hub but causes the hub to rotate by use of gears
rotor: the rotating part of an electric motor
stator:the stationary part of an electric motor
non-geared motor: the outer casing of the hub is an integral part of the motor and usually this outer casing has magnets attached to it (it acts as a rotor)
freewheel: a. Geared hub motors: a mechanical device which allows the hub to rotate freely in one direction without causing the internal motor to rotate. This means pedalling is easy and coasting has very little resistance.
b. Non-geared hub motors: freewheel refers to how much resistance the bicycle wheel has when rotating with no motor power (since the motor and hub are one and the same if the wheel is turning the motor is also turning), there is no mechanical freewheel system involved
cogging : applies generally to non-geared motors and is the resistive force acting against rotation of the wheel, it is caused by the reaction of electrons in the iron core of a motor to the rotating magnetic field of the magnets on the outer rim of the hub.
It will be felt as a small force acting against when you pedal when the motor power is off.
back emf: is the current produced in a motor by magnets moving past coils, motor is acting like a generator. When current is applied from batteries it overcomes the back emf, unless motor is rotating faster than top speed caused by battery current, then back emf is bigger than battery voltage.
emf: (electro motive force): force current produces as its induced magetic field interacts with permanent magnets magnetic field.
inductance: when current is turned off the collapsing current makes a collapsing magnetic field which creates a high voltage spike.
voltage spike: can be associated with inductance when a current flowing through a motor is switched off. If a power wire to the motor accidentally disconnects or breaks while motor is under load a large voltage spike may occur and can damage mosfets in controller circuit
saturation: the iron core of a motor can only absorb a certain amount of magnetic field, at a certain point it becomes saturated and this determines the limit of power the motor can produce.
brushless motors: generally have 8 wires coming out of them. Three thick wires which are for motor power(the windings). Three wires because the motors have 3 sets of windings in them and hence are called 3 phase motors. The other 5 wires are for the hall effect sensors ( one positive power wire, one negative ground wire and the other three wires are for each phase of windings which each have a hall effect sensor.)
brushed motors; usually have only two wires, one positive and one negative. They have carbon brushes which contact a rotating segmented drum which switches which coil is recieving current from the battery.. Brushed motors are generally also 3 phase motor because they have three sets of windings.
commutator: rotating drum made from copper segments which switch the coil in motor which is recieving power at any time.
and hence maintain the revolving of the motor.
brushes carbon(graphite) blocks which conduct electricity but are very slippery (low friction) so copper commutator segments will slide along without friction (well very low friction). Type of brush used can influence efficiency of motor.
3phase:most electric motors are three phase, it is an efficient method for running a motor. It involves having three separate sets of copper windings in the motor. 3 phase effect discovered by Nichola Tesla.
hall effect sensors: in brushless motors hall effect sensors replace the commutator. It is a method of switching which phase is being given current at any one time. Usually two phases will have power at any given time. Hall sensors allow a small current to flow through them. This hall sensors are switched on/off as a north then south pole passes it. This very small current flowing through them goes to a mosfet which in turn is switched on/off in sync with the hall sensors. The mosfets allow large currents to flow to the motor coils in a very precise pattern determined by their location near the magnets.
resistance: copper wire has a certain resitance to the flow of electrons through it, this resistance is used to determine the number of turns of wire and thickness of wire used in a motor.
windings: This refers to the copper wire in a motor which is usually wound around an iron core.
coils: coils and windings refer to the same thing, the copper wire in a motor.
iron core: the iron core of a dc motor acts to channel the magnetic field and makes the motor run efficiently.
slotted motors: Slotted motors usually have pilars of coils or copper wire wrapped around an iron core.These motors usually have the magnets and coils one inside of the other.
non-slotted (axial motors): these motors usually have an iron backing plate which the copper wire sits on top of in flat coils.
The magnets or the coils may be the stator or the rotor depending on motor design. These motors usually have the magnets and coils lying next too each other.
pwm (pulse width modulation): This is a method for regulating the voltage which a motor 'sees' from the batteries. See controller section for detailed explanation.
diodes: the devices allow electric current to only flow in one direction.
resistors: the devices determine how much electricity can flow through a wire..
capacitors: these devies temporarily store electrical energy
magnetic field: magnetic fields are created by electrons movements or positioning. Permanent magnet materials are surrounded by a magnetic field permanently and is due to how the electrons line up inside the material. Temporary magnetic fields are created when electrons flow through a wire.
induced magnetic field:an induced magnetic field is created when electrons flow through a wire.
current:the flow of electrons through a wire
electrons: very very tiny packets of energy which can travel very quickly and easily through metals.
neodymium (rare earth) magnets: quite strong permanent magnets, usually look silver in colour.
ceramic magnets: about 1/4 as strong as rare earth magnets, are generally dark coloured grey to black.