I'm going to show two side-kicks that we have in Shotokan karate. The snapping side-kick, the yoko geri keage, and the thrusting sidekick, the yoko geri kekomi. The important difference is the knee positioning, and a little bit, the emphasis of the hip, as well. The thrust-kick is more powerful and more penetrative, but of course a little slower. The snap-kick is lighter and quicker, but it rises up a little more, which a little bit trickier to apply.
Let's start with the side snap-kick. You go from here, and the ankle is twisted strongly. You're going to kick with the side edge of the foot with the side-kicks. You need to twist the ankle and get used to the fatigue that you'll get here, because what we really want is, like all techniques, something hard on the end of something quite supple. This knee is going to point to the target, pushing off the floor, like all the other techniques, squeezing the obliques this time to stop your body leaning away. From here, you're going to squeeze, squeeze off the floor. Side snap-kick.
Normally, we're going to be moving along much more. You get the idea of it. Your weight's behind it. The kick is light, so trying to make it heavy is sort of contradicting feeling of the kick. Keep it light. Bend the knee. Point the knee towards the target, which is a basic principle in all snapping techniques. Snap the foot back sharply on the same course as it went out. Going out one way and bringing the foot the other way is not really going to give you the pure form.
The other side-kick is the thrust-kick. Unlike the snap, your heel is pointing, and your back side is going to be pushing behind the striking surface. The return is also going to be different. Instead of flicking the foot back, you're bringing the whole leg back. The nature of the technique is heavy, but like side snap-kick, don't make it heavy. Just the course makes it heavy, more penetrative. Push and pull, much more like a thrust or a punch. From here, push and pull. Out with a hit, back with really the hip (?) flexor and the thigh. You push it out a little bit with the arm. The elbow pulls the fist back. You push it out with the back side. The knee pulls the foot back.
You have side snap-kick, yoko geri keage, side thrust-kick, yoko geri kekomi. The two side-kicks of Shotokan karate.