Although quite brief, "A Clean-Well-Lighted Place" is full of interpretative possibility. One theme is indeed generational difference--a conflict that was also mirrored in 1920s American and Western European culture.
This theme is introduced early in the text. The young waiter is unable to understand how the old man in the story could be depressed since he had "plenty of money." Of course in Hemingway's fiction, a closely examined life reveals a long list of depressing realities.
The young waiter in the story is more concerned about his late nights than with the old man's difficult existence. Unable to think beyond his immediate needs of money and companionship, the waiter notes that "An old man is a nasty thing."
The older waiter is more sympathetic to the old man's plight. Hemingway describes him as "unhurried" (hurry is generally not positive in any of Hemingway's fiction as at implies an inability to stop and savor life's brief moments of beauty and goodness). The older waiter tells his colleague that he has "youth, confidence, and a job." The younger waiter has "everything," but he lacks wisdom. The young waiter rushes home to his wife; the older waiter recognizes that "there may be someone who needs the cafe."
The two waiters represent two different approaches to living. The younger waiter is rash, egotistic, and naive. The older waiter, like the old man, has seen the dark side of life--the death, decay, and loss that is "nada" : "a nothing that he knew all too well." The cafe--bright and dignified--could offer a respite from nada.
It is this awareness of nada that separates the waiters and is here dramatized as a generational difference. This awareness of nada is not only a function of age and wisdom, however, but in this story, the confidence and youth of the younger waiter insulates him from nada. It is, however, a false insulation. In Hemingway, nothingness is pervasive.