What was meant was the "type of service" a passenger would be getting aboard the train. In the above case, if all the comforts of a regular Humsafar train are available to the passenger, then it may be called a "Humsafar Special". Humsafar liveries are very different and more comfortable than other trains.
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If I were to book on this train, then by just seeing the name "Humsafar Special", I would already be looking forward to a more comfortable journey than a regular AC SF.
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For "Rajdhani Special", this logic would work only if all the amenities of Rajdhani are available, for example breakfast/lunch included, high speed, etc.
Thanks.