米 as rice specifically means uncooked rice. Cooked rice is 米饭 or just 饭. 大米 means "rice" as a grain/commodity.
culture
Rice is the staple food of southern China, while northern China traditionally relies more on wheat (面食 — noodles, steamed buns, dumplings). The divide roughly follows the Qinling Mountains and Huai River.
Components
pictograph
米mǐ
rice grain
A pictograph of rice grains scattered on a thresher. The four dots in oracle bone forms were single grains of rice; the central horizontal-and-vertical cross was the threshing pestle separating grain from husk. Functions as Kangxi radical #119 anchoring grain words: 粉 (flour), 粒 (grain), 糖 (sugar), 粥 (porridge). The metric meter usage came in the 19th century as a phonetic loan from French mètre.