Eliyahu in Shas

Some time back, I heard an interesting diyyuk made between two of Eliyahu's primary roles in the gemara with regard to the resolution of doubts.

In some sugyos in dinei mamonos (e.g., Bava Metzi'a 3a), a resolution is reached by saying, "ha-kol y'hei munach ad she-yavo Eliyahu" - in a case where a pool of money is owed to two parties but they argue over who is owed the larger share, R' Yosei holds that neither party gets anything (even that which is undisputed), to provide a disincentive for the party owed less to lie. Rather, the entire pot is put in storage until Eliyahu comes and reveals whose is the larger share.

In other sugyos, doubts are left unresolved by the expression "Teiku". According to several rishonim, the word has a meaning of its own, but the folk etymology of the word is that it's an acronym for "Tishbi y'tareitz kushiyos u'ba'ayos" - The Tishbite will answer all of our questions and problems in halacha that we are unable to resolve.

According to this vort, the two roles are expressed using two different names for Eliyahu. For cases of halachic doubt, we wait for the coming of the Tishbite, the talmid chacham par excellence who is able to resolve our unanswered questions. For cases of doubt in the physical reality, we wait for the second coming of the hidden prophet, Eliyahu. I don't recall why the two names specifically have these two meanings.

I now question the veracity of this vort of unknown origin, though. On Brachos 35b, Rava says that the halachic issue of whether one has to bentch if he is kovei'a seudah on wine will be resolved "when Eliyahu comes", implying that the name Eliyahu is also used to refer to the talmid chacham who will be able to answer our questions.

(I suppose that this may be what some may call a straw-man post, in that I cannot verify the existence of the person who told me this vort, but in the event that someone else has heard this said before, perhaps they can fill in my gap. One could perhaps also mention Eliyahu with reference to the sugya of "choltzin b'min'al" in Yevamos, but I don't think this adds anything beyond the sugya in Brachos that I already referenced.)