During the 'Amidah on Rosh Hashanah, the Yom Tob (Holy Day) of Rosh Hashanah must be specifically mentioned. If it was not, the 'Amidah must be repeated. If, by mistake during the Rosh Hashanah 'Amidah, one were to say Meqaddesh "Yisrael Wehazzemanim" as one does on other holidays, instead of "Yom haZikkaron" which refers to Rosh Hashanah, one must repeat it.
When Rosh Hashanah falls on a week day, we say "Yom Teru'ah" (a day of solemn blowing). If it falls on Shabbath we say "Yom Zikhron Teru'ah" (a day of the rememberance of blowing) since the Shofar is not blown on Shabbath. If, by mistake one said Yom Teru'ah when it should have been Yom Zichron Teru'ah, or one said Yom Zichron Teru'ah when it should have been Yom Teru'ah, one does not repeat it.
(See Shulhan 'Arukh 582:7. Kaf Hahayim ibid, Oth 42, 43, 47)
