1. Question: What is the difference between making a mistake by the counting of the omer and immediately fixing it and making a mistake by the blessing in shemone esray by yom tov and mixing it up with shabbos and immediately fixing it?
A. The Mishna Berura (489:32) says that if one said “today is the fourth day of the omer” and then immediately realize it is the fifth for example he just has to say “the fifth day of the omer” and not start from the beginning of the statement. B. The Mishna Berura (487:3) says if a person mistakenly said “mikadesh hashabbos” in his yom tov shemone esray instead of “mikadesh Yisrael vihazmanim” he must go back and say “mikadesh Yisrael vihazmanim” and not just say “Yisrael vihazmanim” immediately, when he realizes his mistake.
C. On a yom tov That falls out on Shabbos we say in our shemone esray “mikadesh hashabbos Yisrael vihazmanim”.
Answer: On Yom Tov it’s not recognizable that you are fixing the mistake if you just say the correct endings soon as you realize your mistake therefore you have to start from the beginning of the statement. But by the omer it’s obvious that you are fixing your mistake because you never count twice. (See Dirshu Mishna 489:32 footnote 68.)