How do ∀x [P(x) ∨ Q(x)] and ∀x [P(x)] ∨ ∀x [Q(x)] differ in their meaning?

Question

How do ∀x [P(x) ∨ Q(x)] and ∀x [P(x)] ∨ ∀x [Q(x)] differ in their meaning?

I thought it was because when ∀x is defined twice there is a possibility of a different x value for both P(x) and Q(x) but then I noticed it was for all so this would not be the case as it would use every x value.

Could you have two different sets of x?

Answer 1

Suppose P(X) means "X is even" and Q(X) means "X is odd" and assume you're taking about integers. Is the first formula true? How about the second? Does that explain why they're not the same?