The Ulster and Delaware, until it was taken over by the NYC in 1932, showed a station number in the Employes Time Table, along with telegraph office calls and open hours, on pages separate from the schedule pages. The schedule pages showed the station milepost to the nearest mile and tenth. The station numbers corresponded to the nearest milepost on either side of the station, measured from Kingston Point. The Kaaterskill and Hunter Branch stations carried a prefix of A with the station numbers, measured from Phoenicia.
That practice of showing station numbers in the time table ended with New York Central ownership, but the Catskill Mountain Branch crews still referred to the stations by their U&D numbers right to the end of service on the branch. When they switched out their train in station order at West Hurley, the conductor chalked the destination station number on each car to make the switching easier. Stamford was 74, Hobart was 78, and Oneonta was 106, for instance.
I believe the U&D, being a fairly simple operation, used these station numbers on conductor's wheel reports and for car movement accounting. The NYC, being much more complex, published a list of station numbers, listed by branch or subdivision, to be used by agents and conductors to account for car movements. They were larger numbers, five digits if I remember correctly, and they did not correspond with mile posts. The list was published by the Auditor of Freight Revenue for the use of conductors, agents and accountants.
There was also a nationwide tariff, the Official List of Open and Prepay Stations, called "Leland's Tariff" after the name of the issuing agent, that showed a number for every railroad station in the U.S., along with an official number for each railroad company (NYCRR was 540). I think the station numbers in Leland's Tariff did not correspond with the numbers used internally by the NYCRR accounting department.
If someone has copy of a NYC Conductor's Wheel Report, the Accounting Department station list and Leland's Tariff, they could give us a definite report on whether the numbers correspond. Those are a few items that slipped by this packrat in ages past.
Gordon Davids