Each are symbols of education. One, the First Academy Building, is where the boys formal education takes place. Everything from academic classes to decorum is learned in this building. Throughout this story, Gene's reliance on having superior expertise in this type of education is threatened.
The tree, for example, teaches Gene truths about life. This is the place where friendship was kindled and threatened. This is also a place where young men went to learn how to really exhibit their bravery and become men as they jumped off the branch. Many were too scared. Gene learned significant lessons here about his choices and the consequences these had on other people.
Another way that these symbols relate has to do with the story's two main characters. The First Academy Building represented all Gene aspired towards: success, intellect and social appropriateness. The tree represented the life that Finny longed for and never received. Finny had hoped to fight in the war. Jumping off the branch as the boys did simulated jumping out of planes. This tree also did not require superior grades or man-made expectations. It simply longed for nature to take its course. Sometimes nature is not so kind and it certainly took its course with Finny.