What is the name of the "group" that differs with each amino acid?

The R organic group.

Explanation:

Amino acids are a complex of organic compounds that combine to build proteins. The general structure of an amino acid is set by a carboxyl group (-COOH), a basic amino group (-NH2), and an organic R group, unique in every amino acid.

The amino acids differ from each other in the particular chemical structure and organization of hydrogen, nitrogen, carbon and oxygen atoms present in the organic R group.