Is $E[Y|X=x]$ a random variable for random variables $X$ and $Y$

Question

For random variables $X$ and $Y$, I know that $E[Y|X]$ is a random variable. If we see $E[Y|X=x]$, is this no longer a random variable, but a constant, because $X$ now is realized by $x$? Or is $E[Y|X=x] = E[Y|X]$

Answer 1

$\mathbb{E}[Y|X=x]$ is a constant for every fixed $x$ whereas $\mathbb{E}[Y|X]$ is a random variable. The relation between the two is that, if $g(x) = \mathbb{E}[Y|X=x]$, then $g(X)=\mathbb{E}[Y|X]$.