I’ve noticed in both the Artscroll and the Koren Siddurim, that there’s a difference between “Yaaleh v’yavo” in the Shmonei Esrei and in Birkat Hamazon. In the Shmonei Esrei, we say “kAel melech chanun” every Rosh Chodesh and Chol HaMoed day, but in Birkat Hamazon, it says we only add “melech” on Rosh HaShannah. Is this correct? If so, what is the reason for it? Thank you!
Interesting question. I’m sure that you also noticed that there are many siddurim that have the same text for BIrkat Hamazon as for Shemona Esrei. The answer to this is because there are different opinions if we should use he word melech in Ya’aleh V’yavo of BIrkas Hamazon. Some say that it is fine and therefore both Shemona Esrei and Birkas Hamazon have it, however others say that it isn’t correct to have the word melech in Yaaleh Vyavo of bentching. The reason is since we already mentioned “malchus bais Dovid” which is the kingship on earth in this bracha, we don’t want to mention the kingdom of H-shem, so it shouldn’t look as if there is a comparison between the two.therefore it isn’t mentioned in bentching.
Regarding Rosh Hashana, I would assume that it isn’t a problem because Rosh Hashana is a day that H-shem’s kingdom is evident, and we spoecifically want to mention His kingdom, therefore on ROsh HAshana everyone says it.
Siddur Otzar Hatefilos (on Shemona Esrei) in the name of Avudraham (In Birkas Hamazon) HILOchos BrachosShar 1 in the nmname of the Raavad, Shelah pg. 82b, Yosef Ometz 783.