Density, count and panel are general terms in statistics.
Density is the continuous distribution of values over a range by frequency. A common example is the normal distribution. There are other distributions for which tools are available in R{base} and other packages.
Count simply refers to the number, usually abbreviated n of observations. There are many count() functions available in R, many for specialized purposes such as genetics. The most general function that I am aware of is dplyr:count.
Panel is time series data, often referred to as "longitudinal" in medicine and social sciences. Econometricians are especially found of these terms.
Aside from wiki, the R Search Engine is a good resource for finding examples of packages implementing these concepts and the documentation or vignettes may provide additional insight.