"Each other" refers to two whereas "one another" to more than two.

Examples:

Jones and Smith quarreled; they struck each other.

Jones, Smith and Brown quarreled; they struck one another.

Some handbooks and textbooks recommend that each other be restricted to reference to two and one another to reference to three or more. The distinction, while neat, is not observed in actual usage. Each other and one another are used interchangeably by good writers and have been since at least the 16th century.

_{Source: Merriam-Webster Dictionary}