In Statistical Inference by Casella and Berger, I am unable to distinguish between the definition ofa a point estimator and a statistic.
Definition 5.2.1 Let $X_{1}, \ldots, X_{n}$ be a random sample of size $n$ from a population and let $T\left(x_{1}, \ldots, x_{n}\right)$ be a real-valued or vector-valued function whose domain includes the sample space of $\left(X_{1}, \ldots, X_{n}\right)$. Then the random variable or random vector $Y=T\left(X_{1}, \ldots, X_{n}\right)$ is called a statistic. The probability distribution of a statistic $Y$ is called the sampling distribution of $Y$.
This chapter is divided into two parts. The first part deals with methods for finding estimators, and the second part deals with evaluating these (and other) estimators. In general these two activities are intertwined. Often the methods of evaluating estimators will suggest new ones. However, for the time being, we will make the distinction between finding estimators and evaluating them.
The rationale behind point estimation is quite simple. When sampling is from a population described by a pdf or pmf $f(x \mid \theta)$, knowledge of $\theta$ yields knowledge of the entire population. Hence, it is natural to seek a method of finding a good estimator of the point $\theta$, that is, a good point estimator. It is also the case that the parameter $\theta$ has a meaningful physical interpretation (as in the case of a population mean) so there is direct interest in obtaining a good point estimate of $\theta$. It may also be the case that some function of $\theta$, say $\tau(\theta)$, is of interest. The methods described in this chapter can also be used to obtain estimators of $\tau(\theta)$.
The following definition of a point estimator may seem unnecessarily vague. However, at this point, we want to be careful not to eliminate any candidates from consideration.
Definition 7.1.1 A point estimator is any function $W\left(X_{1}, \ldots, X_{n}\right)$ of a sample; that is, any statistic is a point estimator.
What would be an example of a point estimator that is not a statistic? My thinking is that a statistic is any measurable function of a random sample and a point estimator is (informally) measuring the parameters of a distribution. This doesn't make sense though as their point estimator definition encompases all of the definition of a statistic.