Kevin is correct, the second train is a SEPTA train however for the next several weeks, SEPTA is doing construction on that rail line so they will be using shuttle buses. SEPTA will have people at 30th Street station to direct you.
You would take two trains. First train is the NJ Transist train from Atlantic City to 30th Street Station in Philadelphia. Second train goes from 30th Street Station to the airport. I believe that is a SEPTA train, but I not 100% sure.
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