The additional coils in a Stepper enable finer-grained positioning and a therefore more things to know about. We need to understand how we can create steps in order to get the correct accuracy, torque and be able to select the correct controller.

In the simon game model, each coil is energized in succession. Each coil is also energized @ 100%, causing the motor to move in 90 degree steps. This is called a full step.

If we energise two adjacent coils, the magnet on the shaft will move in between the coils, doubling the resolution to 45 degrees per step. This is called a half step.

We don't have to fully energize coils. We can partially energize them and at different power levels. This creates a ratio of magnetic pull on the shaft. If a coil is at 75% and the adjacent coil is 100%, the ratio is 3:4. The motor will move 1/4 the way between the coils or 11.25% degrees per step. Precisely control the ratio and smoothly transition between the values (using sin waves instead of square) and you get microstepping. The more interesting projects rely on microstepping so keep an eye out for that term in datasheets and articles.

Before this section ends I should admit that I'm a big 'ol liar. Modern steppers aren't 4 coils and a science-class magnet on a pole. They actually have many coils and many little magnets in a tooth-shaped pattern. Here's a gorgeous shot from Adafruit:

That said, for the most part the coils are wired in parallel and the control mechanism is the same.