The simple answer is, all aftershocks are earthquakes, but not all earthquakes are aftershocks.
An earthquake is caused by a sudden slip along a faultline or tectonic plate boundary that releases stress which has built up.
Imagine trying to push a chair with rubber feet around on the lino. You start pushing on the chair with a constant but small amount of pressure - this is you moving the chair like a tectonic plate. The rubber is providing a fair bit of resistance (like the plates do between each other), so the chair doesn't budge for a while, but then suddenly skids forward a bit (that's your earthquake) and then kind of stutters to a halt as the rubber catches, lets go, catches & lets go again (those are your aftershocks) and then finally stops as you aren't applying the same amount of pressure until you catch up to your chair and start applying the pressure again.
The techtonic plates are being pushed around by pretty constant pressure, but at the boundaries they can get a bit stuck on snags on the other plates. When the pressure gets high enough to overcome the friction, it'll give in an earthquake, and then stutter to a halt once the pressure has all been released. In some places you can get slow earthquakes where there don't seem to be many snags, so the plates slide on past each other without much more than little tremors, or you can get bits that have been all locked up for thousands of years, and then suddenly let go with a hell of a bang.
Canterbury has had the big slip, but hasn't quite finished its movement yet. It's still trying to iron out all the wrinkles, and that may take years to be complete - afterall, it hadn't gone in 16000? years.
Here's the seismograph drum record from Canterbury this morning. As you can see, there are still a lot of snags letting go.
Here's Wellington's for comparison.
Once Canterbury's drum records go back to looking like ours, then maybe you can stop calling them aftershocks, but that might not be for years. Chile is still having some quite large aftershocks from last year's big quake.