Earlier quoted context omitted.
In New York you have MTA Metro North, PATH, MTA Subway, MTA Select Bus Service, NJ Transit, etc. Plus things like JFK AirTrain, Amtrak. It's not confusing though --different names for different things. commuter rail vs intra-city transportation. Metro North doesn't share ticketing with the subway even though they're both MTA
NYC and SF aren't comparable at all since NYC is so much larger. But even then, NYC is more well-organized. The majority of the services you mentioned move commuters between NYC and surrounding areas, so it makes sense that they don't fall under MTA. SF separates its bus system from its train system (at least in labeling), and there's more than one train service within the city alone. EDIT: Bear in mind it wasn't alw…
NYC is a single political entity and the primary metropolitan region of the state in which the city is located. The former is true of the City and County of San Francisco -- but that's, by itself, not even a particular big city -- but not the 9-county Bay Area which is smaller, in population, than NYC despite having more than 20 times the land area. And the latter isn't true of SF at all.)
> SF separates its bus system from its train system (at least in labeling), and there's more than one train service within the city alone.
San Francisco's bus and train service are both labelled "Muni".
BART also has stops in San Francisco but is a separate multicounty agency (the Bay Area Rapid Transit District) of which SF happens to be a member, it isn't SF's.