"Each other" and "one another" are alternate ways of saying the same thing. 'Each other' is more common when only two people are involved; 'one another' is more common when more people are involved. However, either can be used in either case without any loss of meaning.
Вывод: разницы никакой, раз сами авторы учебника использовали one another для обозначения двух людей.