Curtail - a bottom stair, longer than the rest, to support a newel
Dogleg - a flight of stairs which doubles back on itself.
Flying - a stair cantilevered from the wall of the stairwell without a newel.
Geometric - a flying stair whose inner edge is curved.
Newel - central post supporting a spiral stair, also the main posts at the beginning and end of a flight of stairs, carrying the handrail. Quite often, the end post is given a twist, much like a barley sugar, known as a monkey twist, while the downward scroll often found at the end of a handrail is known as a monkey tail.
Nose/Nosing - the projecting edge of a tread. A step with a round nose is sometimes referred to as bottle-nosed.
Riser - the height of an individual step.
String - the supports for the steps.
Tread - the horizontal surface of each step. The going is the same thing, but is properly measured as the horizontal difference between successive nosings.
Winder - a tread which is wider at one end.