There is a subtle distinction between the tefillos Mussaf of Shabbos and Yom Tov. Though in both there is a mention of the korbanos to be offered. Yet, only on Yom Tov do we specifically ask for the return of the Beis Hamikdash. On Shabbos, though, we request the return of all of Klal Yisrael to Eretz Yisrael, yet, the Beis Hamikdash does not get mentioned. Why not?
Look in the Rambam, Hilchos Beis haBechira [Ch.1 Halachah 1] “It is a mitzvas asei to build a bayis for Hashem prepared for korbanos and celebrating there three times per year…” We see that not only korbanos but also the concept of gathering for chag is fundamentally part and parcel of Beis Hamikdash.
As we analyze further, we find that the primary role of the Beis Hamikdash is satisfied by creating the kedushas haMakom. See the Rambam there [Ch. 6, halachah 16] “therefore we can offer all of the korbanos though there is no [longer a] bayis built there … because the first kedushah [granted there] lasts forever.”
Please note, the Rambam described two roles for the Beis Hamikdash. One is for korbanos and the second is for chag. Now we must understand this. The Rambam ruled that for korbanos the kedushas haMakom is sufficient. All korbanos may be offered, though there is no bayis built. But what about chag? The Rambam did not discuss if the kedushas haMakom is enough for the dinim of chag.
See the Ramban [Devarim 16:11] that notes, “[The Torah says,] ‘Three times a year all men must come… to the place I have chosen.’ I do not know how to interpret this verse. Is it coming to teach that — after the Beis Hamikdash is built — then only there can we offer the korbanos of chag and not anywhere else? Or does [this verse] teach [even more], that until the Beis Hamikdash is built there is no mitzvah of aliyah l’regel?”
The Ramban does not know the starting point of the mitzvah of aliyah l’regel. If, according to his first interpretation, this mitzvah begins prior to the building of the Beis Hamikdash and just moves exclusively there upon its being built, then clearly one need not have more than kedushas haMakom and have a full chiyuv of aliyah l’regel. But according to his second interpretation, that aliyah l’regel is dependent, and only starts after the Beis Hamikdash is built, then we would need a proof to suggest that aliyah l’regel exists even when there is only kedushas haMakom.
See the Rambam there [Ch. 2, halachos 1-2] that credits Dovid Hamelech with the preparations of makom haMizbeiach. Perhaps kedushas haMakom had started. Yet we find in the Gemara [Makkos 10a], “And Rabi Yehoshua ben Levi said what does the verse [Tehillim, ch. 122] ‘A song of praise to Dovid, I was happy when people told me, ‘Let’s go to Beis Hashem.’ Dovid said to Hashem, ‘I have heard people saying, when will the old man die to allow Shlomo his son to build the Beis Hamikdash and we will go up there every regel? …” The language of the Gemara implies, like the second interpretation of the Ramban, that a full Beis Hamikdash is required to start the mitzvah of aliyah l’regel even if kedushas ha–Makom has begun in the lifetime of Dovid Hamelech.
Now we can answer our question. Only regel has the extra requirement beyond kedushas haMakom of a full, built Beis Hamikdash. So it is only appropriate and required of our Yom Tov Mussaf to mention the return of the Beis Hamikdash. Whereas on Shabbos, though there is no Beis Hamikdash, yet kedushas haMakom is sufficient to allow the hakravah of the Mussaf korbanos of Shabbos and therefore no mention of the Beis Hamikdash need be made.
Along these lines, let’s investigate another nekudah in tefillas Mussaf of Shalosh Regalim. “Galei kvod malchuscha … v’liYrushalayim beis mikdashecha bsimchas olam.” “Reveal your Kingship … and to Yerushalayim, Your Beis Hamikdash, with an eternal simchah.”
To appreciate this passage let us look at the Gemara [Yoma 21b]. “Rav Shmuel bar Inia says, ‘Why does the passuk [Chaggai 1] referring to Hashem’s honor in the Beis Hamikdash say “va’ekaved” and yet it is read, “va’ekavdah”? Why is the written word missing the letter “hey”? This refers to the five items that were missing from Bayis Sheini compared with Bayis Rishon: the Aron and Kapores and Keruvim, fire, Shechinah, Ruach Hakodesh and Urim V’Tumim.”
Let us add a comment from the Gra on the verse, [Bamidbar 22:31] “‘Vayagel Hashem es einei Bilaam.’ ‘And Hashem revealed to the eyes of Bilaam.’ This is distinct from the revelation to Shmuel where the word “niglah” is used. The word used by Bilaam, lacking the hey, is because of a lack of the Shechinah, since he was ‘the one who fell with gilui einayim.’ Shmuel was a full navi, therefore he experienced the Shechinah as indicated by the letter hey.”
Therefore, it seems that our tefillah is to restore the Third Beis Hamikdash — to be like the first one and not the second one. We desire a full Beis Hamikdash with the Shechinah. Therefore the tefillah uses the word “galei” with the letter hey to indicate that we are beseeching a full Beis Hamikdash including all five items that were lacking in the time of Bayis Sheini.
One more idea from the Gra. “The passuk says, [Shir haShirim, 1:4] “nagilah vnismchah vach — we will be happy with You.” This refers to the building of the First Beis haMikdash when the Shechinah was among the Jewish People. So it would seem that the end of this phrase in Mussaf of ‘simchas olam’ is referring davka to that level of the Shechinah; just as was in the first Beis Hamikdash, so too should return in the Third Beis Hamikdash.
It is amazing to note that the gematria of the word “galei” is 38 just like the word “vaekavdah.” Both reflect the experience of the Shechinah as was discussed in Gemara Yoma.