Commonly, the probability density function (pdf) is used when dealing with continuous random variables, while the probability mass function (pmf) is used for discrete random variables.
This also explains why they are called 'density function' and 'mass function' respectively.
However, my professor would talk about a 'discrete pdf' and a 'continuous pdf' instead of a pms and a pdf.
Wikipedia says that the probability density function is usually reserved for continuous variables.
It seems that my professor is not the only one to use the term discrete probability density function. It is also used here.
Is it incorrect to call the probability mass function by the name "discrete probability density function"?
(I would say so because the pmf does not describe a 'density' in the way that the pdf does.)