Unlike Gun Crazy, Tw0 Fang causes a two-shot burst rather than firing two shots at once. This consumes additional ammo and causes recoil as normal.
Shadow of the Seraphs' special effect is additive with Tw0 Fang, effectively increasing the chance that two shots will be fired by the amount listed on the relic. Notably, with a perfect level 62 or above Shadow of the Seraphs relic and an Unparalleled Professional or Rogue class mod it is possible to achieve a 100% chance of double fire with each shot.
Tw0 Fang's effect requires a minimum delay between shots, meaning that it will not trigger at all on weapons with too high a fire rate, roughly 10.0 or above. This includes not only weapons which have a base fire rate at or above 10.0, but also those which are boosted to or above 10.0 by skills, relics, class mods, and/or Badass Rank. Many SMGs and Assault Rifles are affected by this exclusion.