ר”ח

Shalom and thank you for your question. If I understand correctly, you want to know if the bentching, (birchat hamazon) for Rosh Chodesh which falls on a Shabbat is the Rosh Chodesh benching or the Shabbat bentching? It is both, that is, there is regular Shabbat bentching, which is the same exact bentching as the weekday one, with an additional paragraph for Shabbat which starts with the word ‘Retzei,’ and there is Rosh Chodesh bentching, which is also the same as the weekday bentching, but with the addition of a special paragraph for Rosh Chodesh which starts off with the word ‘Elokeinu’. When Rosh Chodesh falls on  Shabbat, both additional paragraphs are said,  the additional one for Shabbat and the additional one for Rosh Chodesh. Sometimes Rosh Chodesh is two days, one day of which falls on Shabbat. In such a case the bentching on Shabbat includes the special paragraphs for Shabbat and Rosh Chodesh,  while the other day of Rosh Chodesh includes the regular weekday bentching plus the paragraph for Rosh Chodesh. Towards the end of the bentching there is also an additional line for Shabbat to be said on Shabbat, ‘HoRachomon Hu yanchilu lyom shekulo Shabbos’ and an additional line to be said on Rosh Chodesh, ‘HoRachomon Hu yechadesh oleinu es hachodesh hazeh letovah v’livrocho’. When Rosh Chodesh falls on Shabbat both additional lines are said along with the additional paragraphs.

To summarize:

There is regular weekday bentching,

Weekday bentching with an additional paragraph and an additional line for Shabbat,

Weekday bentching with additional paragraph and an additional line for Rosh Chodesh

Weekday bentching with two additional paragraphs and two additional lines for Shabbat Rosh Chodesh.