Unipolar/Bipolar Parallel/Series?!?!?

On the schematic of my motors,
It shows what appear to be four separate
coils inside, giving you eight wires terminating at
screw terminals inside the back of the motor.

Does this mean I have four phase, bipolar motors?

Now, when talking of *how* to wire them I
come across a few different types of terminology:
Unipolar and Bipolar, wiring them in Parallel and Series,
and wiring them in Full Winding and Half Winding.

Can someone please explain the difference between these for me?
Here is what I gather so far:
Bipolar has only two wires per "phase" or coil. (correct?)

Unipolar usually has three, but only uses two of them.
One of those being a "center tap" on an otherwise Bipolar coil. (correct?)

To wire my motors in Parallel, I would connect the first wires of
two coils together and the second wires of two coils together. (correct?)
(in my mind - basically stacking the coils on top of each other)

To wire my motors in Series, I would connect the second wire of
on coil to the first wire of the next, and use the remaing two for input.
(correct?)
(in my mind - stringing them together in a line)

What is Full Winding and Half Winding?
Is this an esoteric way of saying Unipolar and Bipolar?

If not, what is it?

Thanks,

Weyland