"Electronic Ignition" is the term for any system that replaces mechanical breaker points with a non-mechanical trigger. This can be a optical sensor where a light beam is interrupted, or a Hall-effect sensor, where a voltage is produced by passing a ferrous object past a magnetic field.
A solid-state "module" interprets the voltage using a transistor(s) to switch the ignition coil primary between closed (saturation of the windings) and open (interruption of current and collapse of the magnetic field across the secondary winding) to create the spark.
A HEI (a GM-term for "High Energy Ignition") system utilizes a distributor cap-mounted ignition coil and distributor-mounted control module to produce a higher voltage (approx. 45kv versus 25-35kv) spark. Spark output can also be boosted by spark amplifiers. One of the main reasons that GM introduced HEI was to be able to run wide spark plug gaps and, thus, better ignite the extremely lean mixtures needed to control HC (hydrocarbon) emissions.
Some of the advantages of "electronic ignition" over breaker points are.....
a. Since no "mechanical" function is needed, other than passing a device past a sensor, there is no degradation of spark at high rpms that could be caused by point bounce and,
b. Also, because of the lack of mechanical interface, no rubbing block to wear causing the point gap to gradually close up, nor arcing at the contacts to cause pitting or wear.
On the other hand, while points gradually wear out, "electronic ignition" components generally fail suddenly and completely, although reliability has improved greatly over the years. Heat is still the worst enemy of "electronic ignition" components.
Note that I did not mention CD or "Capacitive Discharge" ignition systems as these are not typical of automotive applications which, almost exclusively, use ID or "Inductive Discharge" ignition systems, which use an ignition coil(s) to generate spark, versus a large Capacitor.