The reciprocal pronouns in English are one another and each other. Together with the reflexive pronouns — myself, yourself, ourselves, yourselves, and others — they are classified as anaphors.
Reciprocity is the broader concept, of which reflexivity is a special case. Reciprocity has A relating to B and B relating in exactly the same way to A. Reflexivity is the concept of A reciprocating with itself.
Reciprocal: A↔B = A→B and A←B = A→B and B→A
Reflexive: A↔A = A→A and A←A = A→A and A→A = simply A→A
Examples:
Reciprocal: They all said "Hello" to one another.
Reflexive: All alone, he had no friends but himself.
The classical Greek reciprocal pronoun was allēlōn (ἀλλἠλων). From this stems the word parallel : para allēlois "beside each other".