There is no such thing as an axe kick. Shocking, isn't it? After all, we use them all the time, and we even have a Korean term for it - jigeau chagi. But, technically, it does not exist - there is no reference to it in the Condensed Encyclopedia.
What we call an 'axe kick' is in fact an umbrella term covering two or three 'true' kicks. The first is the downward kick, naeryo chagi. This kick uses either the back heel or ball of the foot to attack the skull, clavicle or face in a downward direction, and arcs broadly across one's body in order to clear an obstacle, for instance another person, before striking the target. (At the same time, it may serve to ward off a potential attack from the aforementioned obstacle.)
The next is the pick-shape kick, gokaeng-i chagi. It again uses the back heel against the skull or clavicle. The pick-shape kick is described in the Condensed Encyclopedia as 'a variation of a downward kick'; what distinguishes it is that its motion is directly up-down.
When we say 'axe kick', the term may sometimes refer to a downward kick, and sometimes to a pick-shape kick. At times, an 'axe kick' looks wholly like neither kick, but perhaps somewhere in between, a corruption of the pure techniques. What is required is a drift away from this unorthodox name towards the more correct and more specific terminology.
The other 'true' kick which relates to the 'axe kick' is the straight kick. This is a downward or backward attack with the back heel aimed at the knee. The interesting point here, however, is the Korean - jigeau chagi. Look familiar?
There is no such thing as an outer crescent kick. (Gets worse, doesn't it?) There is, in fact, no such thing as an inner crescent kick either. The 'Swiss Army Crescent Kick' can actually be divided into four distinct kicks. As an attack, the 'outer crescent kick' uses the footsword, and is termed an outward vertical kick, bakuro sewo chagi. The 'inner crescent kick' uses the reverse footsword as an inward vertical kick, anuro sewo chagi. As a block, the 'outer crescent kick' uses the side instep, and is called a hooking kick, golcho chagi. 'Inner crescent kick': as a block it uses the sole, and is called a ... crescent kick, bandal chagi. Not confusing at all, is it?
The straight-legged 'crescent kicks' we often use along with front rising kicks are, of course, not 'outer/inner crescent kicks' either. The word from the Techniques Committee is that these are vertical kick exercises, outward or vertical kick exercises, inward.
At this point, anguished students often cry out in despair, 'But if an outer crescent kick is really a hooking kick, then what's this?' as they demonstrate a Van Damme Special Hook Kick.
There is no such thing as a hook kick.
What is commonly referred to as a hook kick is in fact a reverse hooking kick. To properly explain this, I shall have to shatter some more illusions. Chiefly this: reverse does not mean spinning. (You may scream now.) 'Reverse' has three rough meanings.
In (a), the Korean word used is dung. In both (b) and (c), 'reverse' is translated as bandae. It is commonly thought that a reverse turning kick is so named because the kicker spins around. However, it is not essential for a reverse turning kick to spin. A turning kick comes from the outside of the body and moves inwards. Thus, a reverse turning kick starts from the inside and moves out. It only spins if performed off the back leg.
In a similar fashion, both the 'hook kick' and 'reverse hook kick' are actually reverse hooking kicks, using the front and back legs respectively. And here we have confusion.
'Surely, if a hooking kick is an "outer crescent" kick, and if reverse means "going the other way", then a reverse hooking kick is a crescent kick?'
This confusion is cleared up by the Korean phrasing. We all know 'hook kick' as goro chagi, and reverse turning kick as bandae tollyo chagi, and hooking kick as golcho chagi. Surely 'reverse hooking kick' is therefore bandae golcho chagi? But no. It is bandae tollyo goro chagi.
A 'hook kick' is often described to juniors as a 'side kick that hooks', although any black belt knows this is rather inaccurate. The above Korean terminology defines it as a 'reverse turning kick that hooks'. Another mystery explained.
The bad news is that a back leg 'hook kick' is a technical impossibility, as being a back leg 'reverse turning kick that hooks', it should spin. Thus, we have another kick that does not exist but is used anyway.
The final misconception I would like to discuss is that of the difference between high, middle, low (nopunde, kaunde, najunde), and high section, middle section, low section (nopun bubun, kaunde bubun, najun bubun). Many people might tell you that there is no difference.
These people are wrong.
The definition of a high attack is one in which, to quote the Condensed Encyclopedia, 'the attacking tool reaches the eye height of the attacker at the moment of impact'. Shoulder or umbilicus (navel) height for middle and low attacks respectively. This is irrespective of the height of the target, e.g. the high turning kick in Choong-Jang, performed from a kneeling position.
The measure of height which concerns a target is high, middle or low section. High section includes any point above the target's neck height. Middle section is anything between the target's shoulders and umbilicus. Low section is anything lower than that.
Thus, a high attack against a taller opponent may only reach that opponent's middle section. A low punch against a child might be a high section attack. So while the high turning kick in Choong Jang is relatively easy, a high section kick from the same position to anyone over four feet tall would be all but impossible.