Stair Naming Conventions 
How do we name these vertically-inclined pedestrian pathways?  Are they stairs, steps, stairways, or staircases?  And how do we distinguish one stairway from another? 
Steps, Stairs, Stairways, and Staircases 
These are all names for the same thing.  There seems to be a regional difference in whether one calls them “stairs” or “steps.”  The term “stairs” (or stairways) is generally used on the West Coast.  Examples are the titles of books: Portland’s Little Red Book of Stairs, Stairway Walks in San Francisco, and Stairway Walks in Los Angeles.  Conversely, on the East Coast the term “steps” seems to be the standard.  Books published on the subject on the East Coast are titled The Steps of Pittsburgh and Walking the Steps of Cincinnati
So which is correct?  They are all correct.  I have decided to use the local terminology whenever possible.  So I use “steps” where it appears to be the standard and “stairway” where “stairs” or “stairway” or “staircase” is used.  I selected the term “stairway” over “stairs” because “stairway” implies a collection of stairs (which are sometimes separated by stair landings and/or cross streets).  And I prefer “stairway” over “staircase” because “staircase” is usually thought of in terms of an indoor set of stairs and my focus is on outdoor stairs. 
If I don’t know the local usage then I will use the default term of “stairway.” 
I have discovered that most stairways (steps, etc.) do not have official names.  Or at least they do not have signage at the stairway telling the public what is the official name.  Often the local neighbors will have a variety of names that they use for a stairway, without considering that their local name might be used by someone else for another similar stairway a block away.  For example, in Seattle to use the name “Capitol Hill Stairs” could refer to either the Howe Stairway or the Blaine Stairway, one block away. 
I decided that I needed a site-specific name for each stairway.  In Seattle, where I started this crazy project, the naming is rather easy.  Most Seattle stairways are located in the public right-of-way as an extension of an existing road/street.  So it only makes sense to name the stairway after the street name.  So the stairs at the end of SW Thistle Street in Seattle are the Thistle Stairway.  I drop the “SW” and “Street” from the stairway name to keep the name short and simple.  The exception to this rule is when the street is a number street (NE 52nd Street, for example).  Then, to maintain some minimal clarity at to location, I include the entire street name in the stairway name (NE 52nd Street Stairway).   
Complications sometimes arise when there are two or more stairways on the same street.  For example, in Seattle on Queen Anne Hill there are three major stairways (and one minor one) on Galer Street.  To distinguish one from another I have named them Lower Galer Stairway (#9), Middle Galer Stairway (#10), and Upper Galer Stairway (#11) (see above).  That is easy if they all go up the same hill, but sometimes that is not the case.  In West Seattle (which is part of the City of Seattle) there are two Graham stairways: one headed uphill to the east and the other headed uphill to the west in the Longfellow Creek valley along Delridge Avenue.  The obvious solution is to name one Graham East Stairway and the other Graham West Stairway. 
The above stairway naming rules work well for Seattle, they don’t work for all cities.  I discovered this fact when I went to Portland, Oregon, to document their stairways.  The locations of the Portland stairways are often in the middle of a city block, where there is no street right-of-way and no street name.  In these locations I had to get creative and use the name of the cross street at the lower end of the stairway (for example, Thurman Stairway above) or some nearby local landmark (The Coming of the White Man Stairway named after the statue at the upper end of the stairway). 
Finally, if someone has already named a stairway I will usually use that local name.  Therefore, I usually followed the naming convention in the books I consulted  (Santa Monica Wood Stairway in Los Angeles, for example).  Another example is the Music Box Steps in LA, which are named after the Laurel and Hardy movie “The Music Box” (you may remember Laurel and Hardy trying to move a piano up these stairs).  The Music Box Steps have an official street/stairway sign located at their lower entrance. 
If you find a name that is either inaccurate or differs from standard local usage please bring it to my attention.  Most of these stairway names are not set in stone (with a few notable exceptions) and I will change the stairway name on my web site and maps, if appropriate.