Grammar (Oxford English Dictionary)
[Etymology: < Old French gramaire < Latin grammatica < Greek
In classical Greek and Latin the word denoted the methodical study of literature (‘philology,' incl. textual and æsthetic criticism, investigation of literary history, etc., besides the study of the Greek and Latin languages. Post-classically, grammatica came to be restricted to the linguistic portion of this discipline, and eventually to ‘grammar’ in the modern sense.]
1.a. That department of the study of a language which deals with its inflexional forms or other means of indicating the relations of words in the sentence, and with the rules for employing these in accordance with established usage . . . . [inflexional = syntactic, or
Note: As above defined, grammar is a body of statements of fact—a ‘science’; but a large portion of it may be viewed as consisting of rules for practice, and so as forming an ‘art’. The old-fashioned definition of grammar as ‘the art of speaking and writing a language correctly’ is too wide, because many questions of ‘correctness’ in language were recognized as outside the province of grammar: e.g. the use of a word in a wrong sense [diction], or a bad pronunciation or spelling, would not have been called a grammatical mistake.
3. An individual's manner of using grammatical forms; speech or writing judged as good or bad according as it conforms to or violates grammatical rules; also speech or writing that is correct according to those rules.
4. The phenomena which form the subject matter of grammar; the system of inflexions and syntactical usages characteristic of a language.
Syntax (Oxford English Dictionary)
[Etymology: E < F < L < Gk syntaxis
2. Grammar. a. The arrangement of words (in their appropriate forms) by which their connection and relation in a sentence are shown. Also, the constructional uses of a word or form or a class of words or forms, or those characteristic of a particular author.
b. The department of grammar which deals with the established usages of grammatical construction and the rules deduced therefrom
(convention = a rule or practice based upon general consent, or accepted and upheld by society at large; an arbitrary rule or practice recognised as valid in any particular art or study)