I know that WRF has many different uses and options, from atmospheric chemistry to uses with fires, and so on. What exactly denotes a parameterization? For example, in WRF-Chem, is the chemistry considered a parameterization? If not, what separates a mechanism from a parameterization? Is photolysis a parameterization? Are the biogenic emissions parameterized?
As defined in the AMS glossary, a parameterization is a simplification of one or several processes in a model. I add that a parameterization commonly adds an error and increases the uncertainty in the model results. In most cases, a parameterization is not derived from physical laws but a fit to data.
These simplifications are employed for different reasons. You probably know the following examples and this answer could have been shorter ;-) but I added them for other readers who might not be aware of them.
Parameterization due to spatial constraints
When we model meteorological and atmospheric chemistry processes in a certain domain, we split this domain into individual grid cells of a given size - such as grid cells of 10 km x 10 km size. Some atmospheric processes have a lower spatial extend than the grid cells - such as small scale turbulence and clouds smaller than 10 km. These things cannot be explicitly calculated by the model (except if we reduce the model resolution). Therefore, we approximate these things taking place on a spatial scale below 10 km. These approximations are denoted as parameterizations.
Parameterizations due to computing effort
When we consider processes such as particle formation, growth, and coagulation we could consider every particle or even every molecule in a model. However, in real world atmospheric applications we have too much particles than we could consider them individually. Therefore, we need to calculate the growth of particles on the base of some parameters and apply it on (log-normal) particle number/volume/... distributions.
Parameterizations due to missing and condensed information
Biogenic emissions are a nice example. We do not know exactly where which trees and plants are located (and which atmospheric conditions like humidity and temperature prevail). For some regions we know it: e.g. for the city of Hamburg there is a detailed (non-public) tree inventory existing. When we do not have this information and work in a gridded domain (i.e. 10 km x 10 km) we need to make a simplified assumption - such as 10% of the grid cell ground is covered by urban area, 30% by grassland, 10% by desert and 50% by forest (of which 70% are pine trees and 30% other trees). From this information and the average ground level temperature and humidity we need to estimate the amount of various emitted volatile organic compounds. Doing this, is a parameterizations because we over-simplify the actual real world.
From my feeling I would describe a process representation in a model as explicit/non-parameterized when it is included according to the best current/state-of-the-art knowledge. In contrast, when it is considerably simplified, I would denote it as a parameterization.
However, when we presented gas phase chemical processes by differential equations - like as it is done in the gas phase chemistry mechanisms of chemistry transport models -, I would not consider it as parameterizations because due to a large number of identical molecules (and the law of large numbers - probably) we do not actually introduce a large error.