Lag is the downtime period after performing certain attacks or maneuvers. While in the lag period, a player cannot attack or move, and he or she is completely vulnerable to the attacks from an opponent. Different attacks have different lag-times, with the general rule of thumb that more powerful attacks (such as Jigglypuff's Rest, Ganondorf's Warlock Punch, or even Capatain Falcon's Falcon Punch) get longer lag times.
Hitlag, refered to on the Dojo as "impact stall", is the amount of frames between the time you get hit and when the knockback actually occurs. Most hitlags are only a few frames, but some hitlags are quite long, such as Samus' fully-charged charge shot; and in Brawl, Zelda's Lightning Kicks and Captain Falcon's Knee Smash. These attacks have approximately 30 frames (half a second) of hitlag, which is easily noticed in real time. This lag will still affect the attacker even if the attack deals no damage, such as versus Mr. Resetti, stage elements, or a character that is invincible. In addition, when two similar attacks clash and "clink", or an attack is Perfect Shielded, it will produce slightly longer hitlag.
During the hitlag, it is possible to use a technique known as Smash DI, which is where you input a direction during the hitlag, and immediately go in that direction, regardless of the initial knockback direction. It is also possible to perform Multiple Smash DIs, which is best represented in the Perfect Control video on Youtube, at about 2:36, and a slower version at about 3:51, during the credits.
Not to be confused with hitlag is hitstun. Hitstun is the state after a character is hit with an attack and is immoble during knockback.
Notably, most electric-based attacks cause a decent amount of hitstun and hitlag.
In Super Smash Bros. Brawl, when playing on Wi-Fi, there is a delay between pressing the button and your character performing the action. This was subject to huge criticism due to the fact this throws off timing for advanced combos, and makes guarding and evading attacks on time more difficult. Depending on the distance between the players, the lag becomes greater or less.
Screen lag is not a product of Super Smash Bros., but of the equipment that is being used to display it. Some HDTVs and computer monitors have a short delay in displaying the game actions. While in some cases (especially when digital recording is being used) this delay can reach levels that make the game unplayable, other times it is a minor amount that can be tolerated. In fact, some players intentionally practice on a screen with a delay to improve their reaction time and predicting skills.
On several HDTVs, the lag appears to be caused by the deinterlacer, which converts interlaced video to the progressive video that LCD, plasma, and DLP displays expect. Most deinterlacers are designed for non-interactive video such as television and DVD movies; they buffer several frames to determine how best to handle each part of the picture. Wii owners can use a component video cable and progressive display mode to skip the deinterlacer, which noticeably reduces this lag in Melee and Brawl on TVs such as a Vizio VX32L.