These two are reciprocal pronouns.
We use the reciprocal pronouns each other and one another when two or more people do the same thing.
Traditionally, ‘Each other’ refers to two people. Similarly ‘One another’ refers to more than two people.
· He and She look at each other.
· Mary and Rani like each other.
· Joseph, Peter and John like one another.
Standard dictionaries recognise the terms ‘Each Other’ and ‘One Another’ as interchangeable.
In spoken English, there’s no harm in following the traditional” rule. At the same time there’s no harm in ignoring it.