Fox-trotting
Fox-trotting is the technique in all four Super Smash Bros. games that consists of moving along the ground by repeatedly executing characters' initial dash animation, as opposed to using their full dash. Since some characters' initial dash animations move them faster than their full dash, these characters are able to run faster with the use of fox-trotting. Fox trotting is predominately used in Super Smash Bros. Melee, and characters with which the technique is most commonly executed are Fox, Captain Falcon, Roy, and Marth.
One way of performing a fox-trot is by flicking or tapping the control stick sideways to perform an initial dash, returning the stick to a neutral position to cancel the onset of the full dash, and then tapping the stick sideways again to perform another initial dash. This sequence can be repeated to move the character along the ground, and the timing of each character's fox-trot is different. In Super Smash Bros. Brawl, there is a small possibility that characters will trip during their initial dash animation, thus fox-trotting increases the risk of tripping.
In Super Smash Bros. Melee, fox-trotting can also be performed by jump-canceling a dash into a wavedash, then dashing again, or by dash-canceling a full dash into another dash.
Fox trotting is considered slightly more difficult to perform consistently in Smash 64 due to the differences with the initial dash animations.
Dash-sliding
Dash-sliding, a term coined by Clan, Hoboking, and Legend of Brawlcentral, is a variant of Fox-trotting, and is described as a constant state of dashing. It is done by mashing the control stick in a direction, and then returning it to neutral, then repeating, similar to a Foxtrot. It differs from a foxtrot in that when doing a Foxtrot, a dash-dance was needed to change directions. In a dash slide, it is possible to shield cancel out of it. Also, since most characters hunch over in the animation, the player is a smaller target for an added bonus. This can be used as a mindgame, or as a speed advantage over the player's opponent.