It's the same as in Tap dance (with sometimes a nuance on the meaning of "step", in Tap dance you take care of ball or heel contact with the floor and then have a "(Ball)Step" (default) or "(Heel)Step" or "(Flat)Step", in some swing dance you can sometimes do a step in place by first putting the ball on the floor and then drop the heel (of the same foot) in a continious motion ending with a flat foot on the floor with body's weight on it, flat meaning ball and heel contact with the floor):
"kick-step" means that first you do a "kick" (for example imagine you kick in a ball) with your free leg (a) (the one you can raise because it hasn't the body's weight on it) which remains free after that, and second you do a "step" with this free leg/foot (a) which then takes the body's weight on it.
The counts can be (kick(3)-step(4)).
"kick-ballchange" means that first you do a "kick" with your free leg (a) which remains free, second you do a "(ball)step" with foot (a) a little behind, third you do a "step" with the other foot (b) retransferring weight on foot (b).
The counts can be (1&2) (with & meaning between the beats), and for example the "kick-ballchange" (1&2) can replace a "rock step" (12) (or take it (5&6) and (56) if you count the "rock step" at the end).
I say "can".
About "single step" versus "triple step", one can have a look at this topic.
If I collect here some of my posts from there:
Two points are discussed here about the basic steps in ECS:
About the three basic steps (single, double, triple) (which one would be the fundamental basic step, which one to choose depending of the mouvement, which one to choose depending of the music).
About the "rock step" being a the start or a the end of the move (argument in the move itself, argument with the music).
About the three basic steps (single, double, triple):
There seems to be three basic steps in ECS ("single" (rock step, step, step), "double" (rock step, tap step, tap step), "triple" (rock step, triple-step, triple-step) (1-2, 3&4, 5&6)), but this is the same dance because the moves are the same (I guess) so you can choose the basic step you want (and even mix them) when you want (and your partner can make another choice).
Which one is the fundamental one?
An instructor can choose to teach the "single" basic step first because it seems to be easier than the "triple" one and the students can begin to dance more quickly, so they don't quit, but if you are really interested in swing dancing you'll have to learn the "triple" anyway (so why not work it and get it earlier).
Why is the "triple-step" so important?
On a technical dance point of view, it's a powerful tool to move (translation, rotation with translation) (it's quite a lot more powerful than the single step or tap-step by which you're really somewhat limited), it's more precise (you've got three steps to ajust your movement), you have more ways to do it and many kinds of triple-step (for example notice that the basic steps of salsa dance are a kind of "triple-step"), it opens you to a whole new world of possibilities.
You get a really new sensation (after mastering) (and it's interesting to contrast with the feeling of the single step, so knowing both is better) (and in case of the "triple" basic step (rock step, triple-step, triple-step) the contrast between the "triple-step, triple-step" and the "rock-step" is interesting too and you haven't one in "double"), so after tasting (and mastering) you would say "I wouldn't have missed it".
Your timing frame is also more precise with the "triple-step" always in your head.
On a musical point of view, it's good too.
And you'll need it in Lindy Hop and West Coast Swing.
Which one to choose depending on the movement?
The question is what will I do on 3-4 (triple-step or tap-step or step) and idem on 5-6, for example, for a translation move the triple-step is a powerful tool and the tap-step is not going to make it easy, if you don't need to move you can do a tap-step, the single step can be more lengthy or allows you free moves with your free leg.
Which one to choose depending on the music?
I disagree with the tempo argument I always read (for example the music is too fast I can't do the triple, so I do triple-step on slow and single step on fast), because technically there are ways to do triple-step very fast.
According to me it's more about the music itself, for example, a single step is more appropriate to a slow continious sound than a triple-step, and when you have lots of things happening quickly in the music you can do fast footwork (with a lot of small steps and kicks).
About the rock-step begining or ending the move, I thought about it (a long time ago) and I'm convinced that the rock-step must begin the 6 count move.
Argument in the move itself: the rock-step prepares the next part of the move (as well explained by DWise1, glad to find his and him).
Argument in the music, it doesn't matter that much because of the question of the music (measure 4/4) versus the 6 count basic step (it's another story that I'll not tell you in this post) (the point is that the fundamental unit is made of a duration of 2 beats, and you play with multiples of 2, thus 6=2+(2*2)).
Note that if you begin to dance with (triple-step, triple-step) (as your first steps on this song) you can fit it in a measure (at the begining of the story) and I think it's better to take care of the first measure rather than the first beat.
In the 6 count basic step, you have the "rock-step" (2 counts), and then (or before) the (one step, one step) or (three steps, three steps), that is one step or three steps in a duration of two counts:
In the "one step" case you can choose to do this step on the first count (odd) of the two, and then you can do an action that doesn't transfer your body's weight (as "point") on the second count (even), hence "step-point" (or "step-touch" or "step-tap" or even "step-toe" if you like tap dancing) or "step" (if you do nothing on the second count).
In the "one step" case you can choose to do this step on the second count (even) of the two (I've read some call this a delayed step), and on the first count (odd) you can do an action that doesn't transfer your body's weight as "tap" or "kick", hence "tap-step" or "kick-step".
In the "three steps" case, you've got the "triple-step" (with the first step on the first count (odd) and the third step on the second count (even), and the second step between the two).
The general idea is in fact to start with one leg free (respectively left or right) at the begining of the fundamental unit of music for that dance (that is duration two beats, ending on even beat, in the case of swing dance music) and end with the body's weight on this leg (so that the other leg is free) at the end of the unit, thus an odd number of steps, then it can be the turn of the other leg on the next unit.
And you can also put between these units a unit where you end with the same free leg you began with (for example the "rock step" or "step step" in swing dance), thus an even number of steps.
This general concept is valid for many dances (finding for each the fundamental unit of music).