Yes, they are related, although as with many other words, you have many different meanings that only have a loose relationship to a single original concept. The fundamental meaning is a form of the verb "to recede," which means to pull back.
At a school graduation ceremony--or a wedding--the "processional" occurs at the opening, when the participants march into the church or auditorium, and the "recessional" occurs at the end, when they march out.
A little hollow place in a wall, where a decoration might be put, or in a mountain--not deep enough to be a cave--is "a recess."
A "recess" can be a short interruption, pause, or rest in an activity. In a school "recess," the students leave the classroom--just as the wedding participants leave the church in the "recessional." Usually, the word "recess" makes us think of where they are going, out on the playground to play, but they are taking a "recess" from the classroom.
Finally, "recession" is interesting because it is a double euphemism. In the 1800s, a sharp economic decline was called a "panic." That word seemed too strong and alarming, so around the 1920s, to make soften it, they started calling panics "depressions." This suggests a small lowered place on a financial chart. Unfortunately, the Great Depression of the 1930s was so very bad that the word "depression" itself started to sound too unpleasant, and in the 1950s, during the Eisenhower era, in order to make them sound milder, they started to call depressions "recessions." In any case, the idea is that the economy "pulls back."