Confused with basic terms:iid, rv

$\displaystyle x_1, x_2, x_3...x_n$ are iid rvs with $\displaystyle E[x_i] = \mu$ and $\displaystyle Var[x_i] = \sigma^2$

I need to make sure my understanding of this statement is correct.

If X is a rv, then it is a function defined over a sample space.

i = 1,2,3,....n constitute the number of trials of this rv.

$\displaystyle x_1, x_2, x_3...x_n$ are not random variables, but values which the random variable (a function) assumes.

So here's my confusion.

If $\displaystyle x_1$ is only a value, analogous to the range of a function, say, $\displaystyle f(x) = x^2$, what is the actual meaning of

$\displaystyle E[x_1] = \mu$ and $\displaystyle Var[x_1] = \sigma^2$? Is it just trying to imply that these values are all drawn from a RV whose parameters are $\displaystyle E[X] = \mu$ and $\displaystyle Var[X] = \sigma^2$?

Are they liberal with the semantics or is my understanding wrong?

Thanks for your time!