What are the different types of moods in the story “After Twenty Years”?

There are several types of moods in the story. First, we'll define the word. "Mood" refers to the atmosphere of the story and is often inspired by tone. The latter is the writer's attitude towards the subject matter or protagonist (or both). "Mood" also inspires an emotional reaction in readers, so it's quite an important story-telling element.
At the beginning of the story, the mood is pleasant, upbeat, and positive. The writer introduces us to a police officer on his rounds. Based on the diction, the writer has full confidence in the officer's abilities. The police officer is described as "strong and important." He's also a "fine-looking cop, watchful, guarding the peace." The police officer (who we later learn is named Jimmy Wells) is a figure that inspires trust.
The mood changes in the middle of the story, however. At the beginning of the story, we learn that a little wind and rain has contributed to the night chill. As the story progresses, we discover that the wind has picked up and the rain is now falling steadily. In response, people look for shelter away from the elements. So, the mood becomes more tense. We get the idea that something ominous is heading our officer's way.
And we aren't mistaken in our emotional reaction: Bob gets apprehended by a police officer masquerading as Jimmy Wells. At the end of the story, the mood is reflective as well as tragic. Instead of having a nice reunion, Bob gets arrested. Yet, we are touched by Jimmy's words in the letter. Instead of arresting his former friend, Jimmy sends someone else to do the job. In this way, Bob will never have the memory of being arrested by a former treasured friend. Jimmy's actions highlight his thoughtful character.

Initially, the mood of the story is quite mysterious. It's 10 o'clock at night on a damp, windswept street, and adding to the atmosphere of mystery, the street is eerily quiet, as the inclement weather has cleared the streets of people. This makes the lone figure of "Silky" Bob all the more conspicuous.
Yet there's an air of mystery about the man as he stands in the doorway of a hardware store. Indeed, the true nature of the relationship between Bob and the beat cop who strikes up a conversation with him won't become clear until Bob and the man he wrongly thinks is his old pal Jimmy Wells walk past a drug store on the corner and are suddenly bathed in brilliant electric light. Then, the mood changes completely; there is no more mystery, no more secrets. Jimmy Wells was the beat cop that Bob had been talking to earlier, and he tipped off his colleague to allow him to move in and arrest his old friend.