Please read the reference(s) you were given for FDs (functional dependencies).
A FD is an expression of the form "A → B" for sets of attributes A & B. So if A and B are different, A → B is a different FD than B → A.
For a relation value or variable R, "A → B holds in R" and "A → B in R" say that if two R tuples have the same subtuple for A then they have the same subtuple for B.
Is A → B in R equivalent to B → A in R? If A and B are the same set, then yes. But what if they aren't?
X Y
a 1
b 1
{X} → {Y} holds in that relation value. {X} <> {Y}. Does {Y} → {X} also hold?