Does the two first order formula interprets to same meaning?

Question

1. [∀x,β → α(x)]

2. [β → (∀x,α(x))]

Here α(x) is a first order formula with x as a free variable, and β is a first order formula with no free variable.

Answer 1

$$(\forall x) [\beta \implies a(x)] \equiv \text{For all $x$, $\beta$ implies $a(x)$}$$ $$\beta \implies (\forall x)[a(x)] \equiv \text{$\beta$ implies that for all $x$, $a(x)$ is true}$$

You didn't specify the domain for $x$, so your statements already have a problem.
Other than that, the two statements are equivalent.