Difference between Variance and 2nd moment
$$ \mathbb{E}(X^n) = \text{raw moment}\\ \mathbb{E}\left[\left(X-\mathbb{E}(X)\right)^n\right] = \text{central moment} $$ where the 2nd central moments represents the variance.
only equal when $\mathbb{E}(X) = 0$ as with $\mathcal{N}(0,1)$.
Simple: $$\operatorname{Var}(X)\neq E(X^2)$$
The second moment is not, in general, equal to variance.