Based on Wikipedia's definition, I believe that statistical model refers to a certain sort of family of distributions, such as univariate Gaussian distributions in general.
Is there special statistical terminology for the result of applying specific parameters to a given model? For example, if $\mu = 5.48$ and $\sigma = 0.3$, then that's a specific Gaussian distribution. I assume it's not also called a statistical model, though it may represent an attempt to summarize or "model" (in the layperson's sense) some dataset. Intuitively it would seem to be an "instantiated model" though I'm not looking to invent my own terminology unless I have to.