Don't know a complete primer on the black art of airline pricing.

But airline pricing can change many times in one day so duplicate a booking made at a different time can likely result in a different price for many reasons.

As for the availability of a certain fare, for a fare to be offer --
there needs to be a fare filed for the fare class,
the fare class needs to have availability and
all the fare rules need to be meet.
So it could be S9 but it is possible no S fare is filed for DCA .
A fare rule from one airport may not be the same as a "similar" fare class fare rule from another. In a multi-segment trip, the fare rules of each segment may not allow combinability of all potential fare classes. And if this seems weirdly complex, it is, that is airline pricing.