provided that = "if" provided that = "but only if" (I think this is better) / "only if" "Provided that" does sound more formal, so I would say that is the main difference. You are much less likely to hear it in informal conversation and much more likely to hear it in very formal conversation. Ex: We can travel to Europe provided that we have enough money. We can travel to Europe if we have enough money. We can travel to Europe, but only if we have enough money. We can travel to Europe only if we have enough money. *You can also split up "only" and "if": We can only travel to Europe if we have enough money.

Firstly, I think that you have misinterpreted 'if or only if'. That actually means two things, i.e. 'provided that' can mean 'if', and it can also mean 'only if'. Yes, it is slightly more formal. It also makes the 'if' more distinct and clear, to make it more important in the sentence. I suspect you might find that it is often used in speeches, and that the examples you have seen come from reported speech. That is because it is easier to verbally stress 'provided that', compared to 'if'.

Definition of provided: on the condition or understanding (that); providing: I'll go provided that the others go, too. https://www.dictionary.com/browse/provided