Nuts grow from trees and their blessing is “Ha’etz.” Peanuts, however, are not nuts, but legumes. While real nuts grow on trees, peanuts grow underground in pods, similar to lentils and peas. As such the blessing for peanuts is “Ha’adamah:”

בָּרוּךְ אַתָּה יְ‑יָ אֱ‑לֹהֵינוּ מֶלֶךְ הָעוֹלָם בּוֹרֵא פְּרִי הָאֲדָמָה

Bah-rookh ah-tah ah-doh-noy, eh-loh-hay-noo meh-lehkh hah-oh-lahm boh-ray peh-ree hah-ah-dah-mah

Blessed are You, L‑rd our G‑d, King of the universe, Who creates the fruit of the earth.

The after-blessing for peanuts is Borei Nefashot.