Let's look at the definition of the word "parameter" in statistics
Here wikipedia says that
A statistical parameter (or population parameter) is a quantity that can be regarded as a numerical characteristic of a population or a statistical model.
Even if a family of distributions is not specified, quantities such as the mean and variance can still be regarded as parameters of the distribution of the population from which a sample is drawn.
And here it says
It is possible to make statistical inferences without assuming a particular parametric family of probability distributions. In that case, one speaks of non-parametric statistics as opposed to the parametric statistics.
So we can consider quantities such as population mean, population variance as parameters because they are charasteristics of population. Therefore we can also consider them as unknown estimands (an estimand is that which is to be estimated in a statistical analysis i.e. the parameter which we want to find).
But what about the population CDF (or PDF in case of continuous distributions)? (It's not a number, it's a function!)
Can we call popualtion CDF a statistical parameter in any statistical problem? Can we call population CDF an estimand and solve problem that sounds like "Let $X_1, \ldots, X_n$ be i.i.d. sample from a population with CDF $F$. You need to estimate $F$"?
As I guess the above mentioned problem is from non-parametric statistic, right?
I would not call the population mean or the population variance "parameters" when there is no parametrized family of distributions. Certainly estimating the c.d.f. based on the data is done, but I would not call it a parameter.