Old English clif "rock, promontory, steep slope," from Proto-Germanic *kliban (cf. Old Saxon clif, Old Norse klif, Middle Dutch klippe, Dutch klip, Old High German klep, German Klippe "cliff, promontory, steep rock").
Clift has been a variant spelling since 15c. and was common in early Modern English, influenced by or merged with clift, a variant of cleft (n.). Cliff-dweller first attested 1889, American English.