If there is no train from A -> C then passengers will travel from A -> B and then B -> C. They switch trains.
If there is a train which goes A -> B -> C, then passengers will board at A, they will all get off at B (recall that every train consist is emptied at a station, no through cargo remain on the train), reloaded at B and then they get off at C.
Same thing for A -> B -> C -> D. Off at every station, reload at every station.
Passenger traffic depends on two things (primarily): the number of houses in a station's cache (green box) and the number of passenger-demanding buildings at a destination city (museums, churches, stadiums, houses). Passengers do not like to walk long distances to a station. If the house is not within a station's cache, they will not walk to the station. Apparently, there is not a taxi service in RT3.