There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimi- nation have recently been the subject of much philosophical and technical dis- cussion. This paper aims to complete their technical investigation. Grades of indiscernibility are defined in terms of satisfaction of certain first-order formu- las. Grades of symmetry are defined in terms of symmetries on a structure. Both of these families of grades of discrimination have been studied in some detail. However, this paper also introduces grades of relativity, defined in terms of rela- tiveness correspondences. This paper explores the relationships between all the grades of discrimination, exhaustively answering several natural questions that have so far received only partial answers. It also establishes which grades can be captured in terms of satisfaction of object-language formulas, and draws con- nections with definability theory.