Paper link: https://www.linz.govt.nz/resources/research/conformal-mappin...
IIRC, for anyone else looking for a curio, there was one state|county|region in the USofA that used a custom conformal projection for a local grid system pre 1980s .. somewhere outside the regular PLA mapping grids.
Subway maps and bus maps in cities are very typically not geographically accurate map projections .. the focus tends to be on a compact stylisation that represents connections for travel plans.
Historically Roman Road maps were on a scroll and very linear, today the UK underground tube maps are displayed in a manner that aids commuters in making connections.
I'm not all that familiar with NYC subway maps (only there for a short time in the 80s .. and who can recall their youth?) but I remember them being more "graphic" rather than "geographic".
I'm thinking more of a local land projection map that would have been used for local surveying in the days prior to global GPS .. but thanks for the thought all the same!
Compared with something like the London Tube map or Paris Metro map it's extremely geographic.
Most of the common global world projections use conic projections that have a major axis aligned NS and conic slices that are orthogonal to the cone major axis mapped to latitude lines that are East-West.
There are many other types of projections, the older NZ map grid is an unusual one.
Once a projection is used to make a flat map, that map can be rotated about in any direction .. but that's another thing altogether.
You may, or not, enjoy looking through a free USGS projection reference of note:
Map projections: A working manual Synder (1987) https://pubs.usgs.gov/publication/pp1395
The Plate 1 link is to a handy wall poster of a limited number of common projections: https://pubs.usgs.gov/pp/1395/plate-1.pdf