What is the legal basis for distinguishing between the ruling for the fearful person and the traveler who prays while moving?

Primary text

The state of fear is a case of necessity which permits necessary actions, allowing for exceptions. The concession granted to the traveler is a specific allowance from the Divine Law (Shar') without necessitating hardship, thus only permitting what has been explicitly narrated. Since no explicit permission for mounting (which requires action and deviation from the Qibla or direction of travel) is narrated for the traveler, the original ruling of remaining on the default practice applies.