Poisson distribution is a special case of the Binomial (andrewchamberlain.com)

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Is the more accurate statement "The Poisson distribution is the limit of the Binomial as n goes to infinity" not a better summary?

Maybe even better: it is the limit of the binomial distribution as the n goes to infinity with n * p constant, where p is the probability of success.

There is a dedicated wiki[1] page for relationship among probability distributions for anybody interested.