Super Street Fighter 2 Turbo/Canceling (ST)
In SF2, normal moves can be canceled into other normal moves or special attacks. This can be done in mainly two ways: the first of them is to cancel remaining recovery frames of certain moves into another normal move. The other one involves a number of ways of canceling initial frames of normal moves into special attacks.
In the original Street Fighter, special moves were quite hard to obtain. In order to obtain a special move, the players had to perform a specific sequence of joystick commands, then press the correct button. However, the joystick motions and the timing for the button press were strict. When developing Street Fighter II, Capcom's designers added a couple of mechanics which would help players when trying to use those special moves, and many more which had been created for the different characters. First of all, special moves could also be obtained by performing the joystick motion and releasing a button. Secondly, normal attacks were allowed to be canceled into special moves during the first frames of their animations. As a consequence, would a player press a button too early, before finishing the joystick movements, the special move would still come out if he or she released the button after the motion was complete.
Kara canceling is when you cancel the initial part of a normal move into a special or super move. The cancel can be done so quickly that you probably may not even see the normal move come out (but you will still hear it). And up until the first hitting frames appear on the screen, depending on the normal attack used. Also, you do not need to use the same button for the special move when using kara canceling. Say, you can kara cancel a Jab into a special move that is obtained with a Jab punch, but you can also kara cancel a Jab into special moves with any other punches, or even kicks.
For several characters, you can shorten the recovery time of their Strong and Fierce fireballs by kara canceling a Jab or Short normal attack into a Strong or Fierce fireball. See T.Akiba's frame data.) Let's take N.Ken for example. If he throws a Jab strength fireball, the recovery on the animation lasts for 39 frames. If he throws a Strong fireball, it's 40 frames. A Fierce fireball will have 41 frames of recovery animation. However if you kara cancel a Strong or Fierce fireball, off of a standing Jab for example, a glitch game will change the recovery of a Strong or Fierce fireball to the 39 frame recovery of a Jab fireball.
Mash moves are also often done through kara canceling. So you rapidly mash Jab with Honda for example, his standing Jab will come out and you'll hear it, but then the starting frames of that standing Jab will be quickly canceled into Jab strength HHS. You won't see the full animation for the standing Jab because the starting frames will get canceled directly into Honda's HHS. Same thing applies to other mash moves such as Blanka's electricity or Chun's legs.
Kara canceling is extremely useful for T.Hawk's command throw done as an empty throw. If you try to walk up and throw someone with T.Hawk's command throw you have to have incredible timing. T.Hawk's pre-jump animation is three frames. Meaning from the moment you hit the up direction as part of a walk up command throw attempt, you have only three frames to hit a punch button to get a command throw, or else T.Hawk will jump straight up into the air. However you can hit standing Jab with T.Hawk, then input the execution for a command throw, and the starting frames of your standing Jab will cancel into a command throw. This technique even makes it possible for T.Hawk to do walk up 720s or walk up super throws. So you can kara cancel a standing Jab into T.Hawk's super and throw your opponent with a super without buffering the super into a jump or off of a tick.
Kara cancels are very useful for things like auto mix-ups that involve special kara cancels built into whiffed normal throws. The idea with this auto mix-up is that you input a throw command and then do a dragon punch right after the throw attempt. If the throw is successful the throw animation comes out and your dragon punch never appears. If the throw whiffs, because your opponent did a reversal attack, then your throw becomes a normal attack, that normal attack is kara canceled into a special attack of your own, and depending on how good your special attack is you could beat your opponent's reversal. Dealing with O.Ken is nightmarish at close ranges because of this kara technique.
As stated in the ST impact freeze section, some normals have the property that, during the freeze, still accepting commands for special moves. When the impact freeze for the attacker ends, all the remaining active and recovery frames are ignored, and the special attack starts immediately. This is the result of a glitch in the original game, but as of Champion Edition it was even coded into the AI behavior so it would use special cancels in their combos. Special canceling is extremely important, as it allows players to extend their block strings and combos, or occupy space in ways otherwise impossible. Several high damaging combos are a result of special canceling, such as Guile's jumping Fierce, crouching Strong into Flash Kick. It also allows a player to extend their attacking momentum. For instance, Ken or Chun Li can never combo a Hadouken or Kikouken from the tip of a crouching Forward kick, even if they cancel it. However, if the enemy has no super bar nor an invulnerable special move, odds are he or she will have to block the incoming projectile, even though they will have completely recovered from the block or hitstun by the time it approaches. This gives them time to recover from the projectile and act while the enemy is yet again in either block or hitstun.
Some normal attacks can also be canceled into the super move. However, super cancels do not make use of the extended cancel time from impact freeze, so they are much harder to obtain.
Chain Canceling (formerly known as "Renda Canceling")
In Japanese, "renda" 連打 is the word they use for rapid-fire chain combos, like Guile's cr.Short->cr.Short. Rapid fire moves are moves which are allowed to be canceled into themselves. In old school Street Fighter (in the pre-Alpha games), you can not cancel chain combos into special or super moves the way you would a single move. If you chain two cr.Shorts, you can not cancel the second one into special moves immediately. Using kara canceling, however, you can get around this limitation. This is called chain canceling ("renda canceling", in Japanese).
Chain canceling consists of canceling a rapid-fire Jab or Short into another Jab or Short, then immediately kara cancel it into a special move.
An example would be Ken's cr.Short->cr.Short xx super. The input is D Short, D Short, D/F, F, D, D/F, F Short any punch. So in order to do TWO cr.Shorts into super, you actually need to hit the Short button THREE times. That st.Short on the end is being kara canceled into the super, which is why you never see it. Also note that you must go all the way to towards (even though Ken's super motion only requires you to go to down/towards). This is because for chain canceling, you must switch from crouching to standing (or from standing to crouching). Because you started with cr.Shorts, you have to end with a st.Short.
The reason why chain canceling is so incredibly good is because you can hit confirm (wait to see if it hits or not). If the Shorts are blocked, go for a throw or a DP. If the Shorts connect, just continue the combo into super.