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Bipolar means that the current flows in both directions through the windings at different times. Unipolar means it only flows one direction through the windings at different times.
Wheather series or parallel depends on the motor leadout. A stepper with only 4 leads (bipolar) gives you no choice. A motor with 6 leads (unipolar) also gives you no choice as to series or parallel, but you can drive it bipolar by disregarding the center tap. An 8 lead motor (aka bifliar) gives you the choice of parallel/series and unipolar/bipolar.
Putting the windings in series doubles the resistance and the inductance, putting them in parallel halves the resistance and inductance.
There are tradeoffs with the different setups. In my opinion, bipolar parallel offers the best overall performance. But thats just my opinion.