In "An Occurrence at Owl Creek Bridge," they started the story with Farquhar's hanging, to show you what was going on.
The second part goes to show what Farquhar had done to deserve the hanging. He had schemed to get past the picket lines, even though citizens were forbidden, on threat of death by hanging.
The third part was everything that happened in Farquhar's mind as he fell and died.
Now, neither of the characters, in their respective stories, seemed to want to admit to wrongdoing. They appeared to have set that aside, to think about other things. For Bob, it was spending time with his friend. For Farquhar, it was getting back to his family.
The difference between the two is that "Silky" Bob resigned himself to his fate. He agreed to go quietly, and off he went. Farquhar, on the other hand, tried to escape, if only in his mind. He refused to acknowledge the punishment for his crimes.