Back quarter circle or "low", "low-back", "back". Sometimes also called Tatsu, in reference to Ryu's Tatsumaki (Hurricane Kick), performed with a back quarter circle and a kick.
Front quarter or "low", "low-front", "front". Also known as a fireball, this command is used to launch a projectile in many games.
A quick recovery is a term used when a character gets back on their feet quickly after a grounding. It is done differently depending on the game, but usually you have to press "jump" or "down" when the character hits the ground. This term tends to be replaced by the term "Teching a Knockdown".