There’s only one symbol in statistics, p. The same variable represents everything. You just get used to it and figure out which p is which from context. It reminds me of George Forman naming all five of his sons George. Here’s an example I ran across recently where p represents four different functions in one equation:
p(θ | x) = p(x | θ) p(θ) / p(x)
Usually this is done with no explanation, but in the example above the author explains that he’s denoting entirely different functions with the same symbol in order to avoid the “clumsy notation” that being explicit would require.
Sometimes the overloading of the 16th letter of the English alphabet becomes just too much and statisticians break down and use the Greek counterpart, π. So then to make matters even more confusing to the uninitiated, π can be a variable or a function.