TITLE: Difference between Poisson and Binomial distributions.
QUESTION [46 upvotes]: If both the Poisson and Binomial distribution are discrete, then why do we need two different distributions?

REPLY [29 votes]: The binomial distribution counts discrete occurrences among discrete trials.
The poisson distribution counts discrete occurrences among a continuous domain.
Ideally speaking, the poisson should only be used when success could occur at any point in a domain.  Such as, for example, cars on a road over a period of time, or random knots in a string over a length, etc.  We are talking about infinitely many infinitesimally small trials, each having at most one success.
In practice, though, the poisson can be used to approximate the binomial under certain conditions, but it is only a rough approximation. Such as using the Normal curve in place of a Binomial under the right conditions.