John Cook puts it well:
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 [Cook] 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 (pi). So then to make matters even more confusing to the uninitiated, π can be a variable or a function.
He’s right, and I say this as someone who’s done my part to spread this notation. We talk in Bayesian Data Analysis about how to use this notation and why it’s more rigorous than it might seem as first. I really really don’t like the notation where people use f for sampling distributions, pi for priors, and L for likelihoods. To me, that really misses the point. The notation shouldn’t depend on the order in which the distributions are specified. They’re all probability distributions, that’s the point.