Emor & Sefiras HaOmer Insights

The Korban HaOmer is named after a measure, an omer, even though the same volume is used in the Mincha offering and called a tenth of an eifah there. Why did the Torah choose that name here? And why does the counting toward Shavuos start from this offering? Rav Yosef Salant in Be'er Yosef finds one earlier use of the word that answers both. On a flight, an elderly woman hands Rabbi Asaf Prisman a small card with three cartoon pictures, and each one says something about being busy.