1. NFPA 101®, Life Safety Code®, 2021 Edition. Section 3.3.258.7, Definition of Stair Tread Depth: "The horizontal projected distance from the leading edge of a stair tread to the leading edge of the adjacent stair tread."
2. NFPA 101®, Life Safety Code® Handbook, 2021 Edition. Exhibit 7.23, which accompanies Section 7.2.2.2.1, visually defines the components of a stair, clearly labeling the horizontal dimension (equivalent to 'B' in the question) as "Tread depth."
3. SFPE, The SFPE Handbook of Fire Protection Engineering, 5th Edition. Chapter 55, "Means of Egress," Section 55.4.2.2, Stairs. This section discusses stair geometry, where tread depth (run) is defined as the horizontal component of the step. (DOI: https://doi.org/10.1007/978-1-4939-2565-055)