“east of the Jordan.” The literal Hebrew is “upon the face of the Jordan.” But what that means is unclear and debated, including if Elijah was to go east of the Jordan or stay west of it. It likely was a place east of the Jordan, thus the REV translation. The phrase “the face of the Jordan” has the idea of being near to the Jordan, connected to it, so it seems even if Elijah went east of the Jordan he was not far from where the Cherith Ravine ran into the Jordan River (see a discussion in Concordia Commentary: 1 Kings 12-22, by Walter Maier III).
“Wadi Cherith.” A “wadi” is an Arabic word (Hebrew is “nahal” #05158) that refers to anything from a deep canyon or ravine to a quite shallow riverbed. It likely most often refers to a valley or ravine that had a river or brook that ran wet during the rainy season but would dry out in the dry season.