On the Streets of America, there's a lot of references to New York City, which isn't surprising given that the area was once known as New York Street. So it's no suprise to see a subway stop too. But Imagineers took an opportunity to honor Walt Disney himself with a seemingly innocuous prop.
The subway station advertises the W and D subway lines, which stand for Walt Disney and it's another great example of Disney Imagineers paying hommage to the man that started it all.
As for the 18th Street Station, there is no 18th Street station on any of the subway lines in New York either, however there was an 18th street station on the East side line that was closed in 1948. If there's a reference there to Disney in some way, I'm not seeing it but it's clear the Imagineers didn't want to associate any real life subway line or station with the fictional one portrayed in Hollywood Studios.
If you're wondering why there's just a few stairs and then nothing else, remember that the Streets of America is a movie backlot. On any backlot, movie studios build just enough for what the camera can see, so there's no need to build anything more than a few stairs at street level to give the look of this being a real subway station entrance.