The discussion clarifies the differences between binomial and Poisson distributions. The binomial distribution is used for a fixed number of independent trials with two possible outcomes, while the Poisson distribution applies to counting events in a fixed interval where the mean is small compared to the maximum possible. It is noted that the Poisson distribution can simplify calculations in certain scenarios, particularly when the mean number of occurrences is low. Additionally, under specific conditions, both distributions can approximate a normal distribution as sample sizes increase. Understanding these distinctions is crucial for applying the correct statistical model in various contexts.