A stair is any step included as part of a series leading to a different floor or level. When only step is present, the word "stair" is typically not used, since the word "stair" connotes a series of steps leading to a higher or lower elevation. Stairs may consist of a variety of materials, including wood, carpeted wood, steel or concrete, and may exist independently or as part of a staircase.
A staircase is a structure unto itself that holds a series of stairs. The stairs in a staircase usually consist of different parts, independently constructed for the overall support of each step. These parts include stringers, which run along the sides of each stair for support; risers, which make up the vertical part of each step; and treads, which make up the horizontal section where you place your feet.
In addition to having stairs consisting of multiple materials, a staircase may also begin with a firm starter step, or swell step. Additionally, a staircase will typically contain contain a balustrade, which contains a series of vertical balusters, or posts, to keep you from falling off the side, thick starter posts and hand rails. These parts all work together to construct a solitary, firm staircase.
While a staircase contains a number of stairs, the term refers to a single uniform piece of architecture, including the stairs themselves and all of the parts that hold them together. If a series of stairs exist independently, like a set of concrete steps molded on the slope of a hill, it may not be referred to as a staircase, but simply as a series of stairs or steps.