They are often used as synonyms but they are different words with different meanings also.
And how do you prove what is not factual? You don't.
Some facts can be proved. It's also proven that all that is true is not provable - Gödel. I.e., the sets of "true" and "provable" are not identities.
And since this has been proven, you'd have to agree that it is "fact."
Like what?
Gödel
Who's that?
One quote from your hero: "I like Islam: it is a consistent [or consequential] idea of religion and open-minded."[Hao Wang (1997), A logical journey: from Gödel to philosophy, The MIT Press, p. 148]