Is there a difference between a propositional function and a WFF?

Question

These two seem the same, are they? I don't see any differences now, but I'd want to know if there are any.

Answer 1

Propositional function is not part of "usual" mathematical logic terminology today.

Basically, what was originally called "propositional function" is an open formula $\varphi(x)$.

If so, it is correct to say that a propositional function is a formula, but not all formuale are open ones.

E.g. $\forall x(x=x)$ is a sentence (i.e. a closed formula) and thus it is not a propositional function.

Answer 2

A WFF is just a sequence of symbols that is syntactically correct (e.g., "$p\land\lor qr\to$" is not a WFF). As such, it corresponds in a straightforward way to a prepositional function that maps truth assignments to all variables to the truth assignment of the evaluated formula. Then again, $\neg(p\land q)$ and $\neg p\lor\neg q$ are different as WFF, but define the same prepositional function.