There is confusion between normalized functions whose area under the curve is one, i.e., density functions, and probability density functions that are not only density functions but that are measures of probability per unit area. One can have lots of other things per unit area, like concentration. Currently, some authors refer to such density functions as pdf's despite the confusion that this causes. One work around is to just use $f(t)$ or of $f(x)$ or whatever and say that it is normalized. However, the rules for how to use density functions are so well documented for statistics, and just because we are not using just probability models does not mean that we are not using statistics; it is just that not all statistics are probabilities.
It would not be a good idea to call generalized density functions df, as df is used for degrees of freedom. Any ideas here are welcome, odf ordinary density functions, gdf, general density function, nf, normalized function. Not a clue what should be done, but something is needed because a pdf is often confused with randomness even though as an $f(x)$ all it is, is a model, a formula, a shell, that sure can be used as a model for a random variable, but as a model it is not itself random, it's just a function.