In regards to what youre asking about for Dulles Airport, the aero train is the mode of transportatiom between all of the terminals. Dulles is a huge airport and it would take people a very long time to walk from one point to the other without this service. The shuttle is merely a way to pick you up from a desired locstion and take you to the airport. Think of this service more like a public taxi or lyft/uber. It can be cheaper but the timing may not be as convenient for you (i.e. you might be scheduled for pickup several hours before your flight actually leaves)
The aerotrain can take you between the main building and terminals- a,b,c, and z. If your going to or from terminal d, you need to take the shuttle
One is a bus between terminal s. The other is a train. Train is located closer to check in, the other is midpoint between terminals. Reference airport map on Google maps
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Shuttle takes you to airport from city, aero train connects you between flight after check in
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