Rise and run are the two legs of any sloped construction problem — how far up, and how far along. In stair layout the total rise is the floor-to-floor height, and design begins by dividing it into a whole number of equal steps: n = round(rise/target riser) sets the riser count, R = rise/n the actual uniform riser, and the treads number n − 1. A 105 in basement rise at a 7.5 in target gives 14 risers of exactly 7.5 in and 13 treads; on 10-in treads the total run is 130 in and the stringer cuts from √(105² + 130²) = 167.1 in of board.
The pair is then judged twice: by code and by comfort. IRC residential limits cap the riser at 7.75 in and require treads of at least 10 in (IBC commercial is stricter at 7 and 11), while the classical Blondel rule wants 2R + T between 24 and 25 inches and the stair angle between 30° and 37° — the worked design lands at 2R + T = 25.0 in and 36.9°, passing everything at the top of the comfort range.
The same two words scale up to the whole roof: a pitch is stated as rise per 12 inches of run, so rafters and stairs are ultimately the same triangle with different code books attached.