TITLE: What's the difference between a probability mass function and a discrete probability distribution?
QUESTION [0 upvotes]: The Wikipedia page on "probability mass function" says "The probability mass function is often the primary means of defining a discrete probability distribution" (emphasis added).  I was under the impression that those two terms were completely synonymous.  What's the difference between them?

REPLY [2 votes]: The difference is subtle. I think it helps to realize that a (probability) distribution is a more general concept. A distribution is something intrinsic to a random variable and determines/describes the behaviour of it. In contrast, a probability mass function (PMF) is one way to concretely describe the distribution quantitatively. Things to note:

In general, a distribution does not necessarily have a PMF or a probabilty density function (PDF). However, a discrete distribution always has a PMF, and a PMF always describes a discrete distribution, and therefore the two things are basically the same.
You should think of a PMF as just one way to describe/define a dicrete distribution. We could also use the cummulative density function for example, or any other exotic description we can think of.
Maybe you can very loosely think like this: The distribution is what carries out the random experiments, and it might look at the PMF to decide what to do, or it might look at something else.
{"set_name": "stack_exchange", "score": 0, "question_id": 2331954}