Smash directional influence
Smash DI is a type of Directional influence that is performed during the frames of hitlag in which the target is immobile after being hit by the attack. The length of the hitlag varies from attack to attack, from 2 frames to 18 frames (Samus's Charge Shot). Smash DI allows the character to move, which can slightly affect knockback, and can move the character into a wall or ceiling to allow wall and ceiling techs. By pressing different directions on the control stick, the player can Smash DI multiple times. This is best represented in the Perfect Control video, at approximately 2:38, and with a frame-by-frame version at about 3:51, during the end credits.
A subtactic is the quarter-circle DI, which involves inputting multiple Smash DIs by rotating the control stick 90 degrees, resulting in a drastic decrease in knockback. Quarter-circle DI was introduced to the United States by smasher Captain Jack and was once known as Japanese DI.
Smash DI is the only type of DI that exists in the original Super Smash Bros.
Automatic Smash DI
Automatic Smash DI functions similarly to Smash DI, but it occurs the frame after the attack's hitlag ends. The character will move, but not as far as in normal Smash DI. ASDI may be inputted either with the control stick or the C-stick, but if both are being held when hitlag ends, the direction in which the C-stick is being held out prioritizes the Control Stick.
A tactic that utilizes both the control stick and the C-stick is called double stick DI, which involves pointing both the control stick and the C-stick in two different directions so the player can alter the trajectory with the control stick and use the C-stick to control the Automatic Smash DI into a different direction from the direction being held on the control stick. This was later found out to be very useful, such as being used to get the lowest angle of knockback while ASDI-ing straight downward to tech along the ground and survive high knockback hits beyond what is possible by allowing said hit to launch the recipient.