Flight: A series of steps between landings

Nose/nosing: The edge of a tread that extends over the riser. 

Rise: The overall height of the stairs. (From the ground to the door/deck etc)

Run: The overall length of the stairs. (From the top edge of the first stair to the bottom edge of the last stair)

Step/Stair: The tread and riser combined.

Stair/Steps: The term for a series of treads and risers

Stair width: The width of a stair. 

Stair Riser: The vertical part of a step, the flat-upright surface that connects the front of one stair tread (the part you step on) to the back of the tread above it.

Stair Riser Height: The heigt of the stair riser. 

Stair stringer: The diagonal structural supports for stairs.

Stair Tread: The horizontal surface of the stair (the part that you step on).

Stair Tread Depth: The distance from the riser to the edge of the nosing.