According to MathWorld (link): "The sample raw moments are unbiased estimators of the population raw moments".
While in Wikipedia (link) it is said:
...the $k$-th raw moment of a population can be estimated using the $k$-th raw sample moment $$\frac{1}{n}\sum_{i = 1}^{n} X^k_i$$
applied to a sample $X_1\dots X_n$ drawn from the population.
It confuses me because to my understanding estimators are statistics (link) used to estimate some parameter. As such, they are functions of random variables. But the expressions found in the articles seems to be functions of outcomes of random variables, and not of the the variables themselves.
I tend to think that a "sample moment" is 'something' that can be computed directly from a sample (or their corresponding outcomes as I understand from this answer). That means, from specific values. One can define an statistic, and then modify it by replacing the random variables with specific outcomes, and perform a computation. But I feel that this is not the same that the original object.
Can anyone clarify me these subtle differences to understand what is a "sample moment"?