Stairs are built, not floated
Floating floors move; stairs cannot. Each tread is glued and fastened with a nosing piece that wraps the front edge, risers are faced with the same product or painted wood, open sides get returned nosings or a stringer detail, and winders are templated individually. Carpeted stairs often hide a bullnose overhang that is cut back so the new nosing sits flush.
Landings
Floored like a small room, with a nosing at the drop and expansion gaps at the walls, in the same product as the stairs and the floors above and below.
Transitions at the top and bottom
The top of the stairs meets the upper floor and the bottom meets the lower floor; the installer plans the heights so both are flush and the floors can still move.
On the quote
Stairs by the step with the nosing type, landings by the square foot, riser treatment, and the day they add to the schedule.

