Halliday & Matthiessen (1999: 6):
There is a warning to be issued in connection with the term "grammar". It is not uncommon in English for the same word to stand both for a phenomenon itself and for the study of that phenomenon. For example, "psychology" is used to mean both the study of the "psyche" and the psyche itself (so "feminine psychology" means women's psychic make-up, not theories of psychology developed by women scholars). In linguistics, while we do distinguish "language" (the phenomenon) from "linguistics" (the study of the phenomenon), we fail to make such a distinction with the word "grammar", which means both the grammar of a language and the study of grammar. To avoid such pathological ambiguity, we find it helpful to refer to the study of grammar by a special name, grammatics. We will use this term from time to time in order to make it quite clear that we are talking about the model, the theory used to interpret the phenomenon, and not the phenomenon itself.
Thus we can say that a grammatics is a theory of grammar, while a grammar is (among other things) a theory of experience. But to show that a grammar is a theory of experience we use a functional, semantically motivated grammatics, since this allows us to seek explanations of the form of the grammar in terms of the functions to which language is adapted. But this closeness of fit between the semantics (i.e. the meaning) and the grammar does not mean that our grammatics can take over the semantic domain.