Epistemic theories of truth analyze the notion of truth in terms of epistemic notions such as justification. Non-epistemic theories of truth analyze the notion of truth in terms of non-epistemic notions such as correspondence with states of affairs. All these theories aim at truth in the sense that one is concerned with what are the facts, with what is actually the case. But what if truth is not always concerned with what is factual or actually the case? There might be cases where something is truthful without being factful. If so, we should distinguish between epistemic truth (concerned with facts) and non-epistemic truth. In that case the above mentioned epistemic and non-epistemic (e.g., correspondence) theories of truth both aim at epistemic truth. The question then becomes how the notion of non-epistemic truth could be further fleshed out. What are examples of non-epistemic truth (if any) and what are the tools to discover such truths? Paradigmatic examples of such truths may be found within existentially loaded domains as religion, ethics and rhetoric. But possibly counterfactual conditionals can be considered as such as well.
So, in short the idea is that there are possibly (existential or other) situations in which we want to be able to speak legitimately of truth without having to presuppose that there are actual ontological states of affairs in the world that make such speak legitimate. In these situations we thus talk about non-factual or non-epistemic truth. These truths are non-factual indeed, but truths nonetheless. To develop a full account of non-epistemic truth would open a whole new realm of philosophical enquiry.