WHY should it?
There is no world wide term for the many different train systems that can exist in a city,around a city and to and from other cities.

Buses and public bikes can also be called Rapid Transit since both allow citizens to travel places much quicker. Maybe I assume you include walking is faster than crawling. A Ferry boat is faster than swimming. I guess you have never heard of a Sea Bus or Aqua Link

https://www.youtube.com/watch?v=TvZXRxnZ...
https://www.youtube.com/watch?v=9v4ZoKTH...
Many years ago the street car systems of many USA cities interconnected with each other. Every car did not go to the other place. Some where local and others interurban.

Pacific Electric, also known as the Red Car system, was a privately owned mass transit system in Southern California consisting of electrically powered streetcars, interurban cars, and buses and was the largest electric railway system in the world in the 1920s. Organized around the city centers of Los Angeles and San Bernardino, it connected cities in Los Angeles County, Orange County, San Bernardino County and Riverside County.