Hi Bill,
Well, I would say that the way Tez describes the kick above (in the OP) is one area that is not used to kick with! That said, here are a few more places of impact for you:
The flat of the foot (at the ball), used in some systems similar to an Axe-kick, but impacting with the ball for reach rather than the heel.
Inside edge of the foot (again at the ball), utilised in Ninjutsu systems, this is an in-close kicking method typically used in grappling situations as a set-up for a throw (or another grappling technique).
The toes (pointed and bunched together), again utilised in Ninjutsu systems, this "spearing" kick is targeted against softer areas (groin, bladder, inner thigh). Not advised without some pretty serious conditioning, however it's great with todays modern steel-capped boots!
Hmm, actually, the only practical use I can think of for the "below the knee, pushing action" described above.... we have a technique called Ashi Dori, or Ashi Dome (Capture the leg/Stop the leg) in which your foot is placed on the ground behind theirs (from the front), and you hook their leg. By pressuring forward, you can create a form of knee-bar. Don't know if you'd class it as a kick, though, we tend to think of it in the grappling skills.
Then you have multiple applications of such impact points. For example, the heel is used as a stomping kick forward (foot turned out), a stomp down (to damage an ankle, or another target present), a hooking inwards kick, a hooking outwards kick, a double-stomp (with an accompanying leap), and a few more. And that's just us again, many other systems have other uses as well!
All that said, though, once again I would point out that a martial art is not defined by it's techniques, a martial arts techniques are defined by the system. So while it can be interesting to know them all, it really doesn't matter that much, so long as you can express your own system, you can use anything (that the philosophy of your system agrees with!). Of course, with yourself, I think that's the case anyway.