Nicely explained Hoppy, and then there are the engines fitted with an electric starter/generator, known as a VFSG, or Variable Frequency Starter Generator. The GenEx and Trent 1000 engines use these on the Dreamliner and have 2 units fitted per engine. They are quite complex pieces of kit (not to mention expensive!
) as once the units have started the engine, they convert into generators to supply the aircraft with electrical power.
See here:
787 Propulsion System