D is a set of prescriptions for what Christopher J. Date and Hugh Darwen believe a relational database management system ought to be like. It is proposed in their paper The Third Manifesto, first published in 1994 and elaborated on in several books since then.
D by itself is an abstract language specification. It does not specify language syntax. Instead, it specifies desirable and undesirable language characteristics in terms of prescriptions and proscriptions. Thus, D is not a language but a family of both implemented and future languages. A "valid D" must have a certain set of features, and exclude a different set of features which Date and Darwen consider unwise and contrary to the relational model proposed by E. F. Codd in 1970. A valid D may have additional features which are outside the scope of relational databases.
Tutorial D is a specific D which is defined and used for illustration in The Third Manifesto. Implementations of D need not have the same syntax as Tutorial D. The purpose of Tutorial D is both educational and to show what a D might be like. Rel is an implementation of Tutorial D.
There are numerous implementations of D, with varying degrees of maturity and compliance.