"each other" and "one another" are different 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.
These must be used only in the plural. The action goes from one person to another, different person; and the reverse.
RIGHT USAGE :
: They love each other. They love one another.
: They write to each other. They write to one another.
: She writes to each other. He loves one another.