Truefully vs Truthfully -- interchangeable?

Are truefully and truthfully essentially the same?

Does one have an implication, intonation, or standard use that the other does not?

I know from Oxford's online dictionary that trueful is an actual word. However I can't tell if it has a history, or if they've included it due to common use (or perhaps misuse?)

The OED says trueful is rare; it says truefully is obsolete. The first, the OED notes, was formed in English (c. 1325) from "true" (meaning faithful in the sense in which we use it today with reference to, for example, romantic relationships).

The primary definition of trueful in the OOD (to which you link) is "loyal, faithful", which is of course different from "honest," the basic meaning of truthful. Thus they are in no way "essentially the same" or "interchangeable."

"Trueful" may be in a dictionary, but it is a very very very unusual word (I don't remember ever having encountered it, and I've certainly never said it).

GloWbE, the corpus of Global Web-based English, has precisely 4 instances of "trueful" and 4 of "truefully". Contrast that with 8608 for "truthful" and 3920 for "truthfully".

I strongly suspect it is a mishearing of "truthful", but it may have entered some people's normal language.