The dictionary says that "cerro" means hill in Spanish, but here in Peru they use it for mountains as well.
I think it actually can mean mountain as well as hill. The proper name for the highest mountain in South America is after all Cerro Aconcagua. Same with the second and third highest peaks, Cerro Ojos del Salado and Cerro Pissis. There is also Cerro Torre, Cerro Chirripo, etc, so I believe the dictionary is in error and it does mean mountain.
I wasn't aware that the ones you mentioned were called cerro as well, so it sounds like the Diccionario Oxford Compacto needs to make a correction! Thanks.