Not a mathematician or logician, but my understanding of it is that there are propositions such that it can be proven that there's no way to prove them either that proposition or its negation. Since either a proposition or its negation must be true, there are therefore true statements that are unprovable. That's the difference between such statements and ones for which a proof just hasn't been found yet. The former are fundamentally unprovable and the latter are not necessarily unprovable. I think that also gives us a sense in which we could possibly state that there are true statements that could NEVER be proven true. I'm not saying that Godel actually showed this, but if someone could find a statement such that both that statement and its negation were unprovable in any formal system, then we would know that there's at least one true statement that's unprovable in any formal system. We just wouldn't know whether that true statement is our original proposition or its negation.
...there are propositions such that it can be proven that there's no way to prove them either that proposition or its negation.
Right, those are 'undecidable' propositions (within a particular formal logical system). Gödel propositions are of that type. Indeed, the title of Gödel's famous incompleteness paper is "On Formally Undecidable Propositions of Principia Mathematica and Related Systems". See post #18 above.