Grammatical studies are usually done with a certain aim in mind, and grammatical descriptions vary with them.
There are two main purposes people describe the Grammar of a language. One type of descriptions is made to understand it, and the other is made to teach it.
When people use a Grammar to learn or to teach a language they expect that it should provide suggestions how to build and use forms of words, word combinations and sentences. Such Grammars are sets of rules. Possible variant of grammatical descriptions of this type depend not only upon the linguistic philosophy the author employ but also upon the philosophy of teaching. The main property of such Grammars is the idea of correctness. As a result these Grammar are usually slightly beyond the time that is they recommend variants that are slightly outdated. E.g. not long ago all Grammars of this type recommended to use the Nominative of the Personal Pronouns in the predicative position (It's I), though the Objective Case was already use in this position (It's me).
Because such Grammars suggest rules they are known as prescriptive Grammars. Of course they are based on the material provided by Grammars of the other sort, of the descriptions made to understand the Grammar of a language. But prescriptive Grammars make selection of the fact presented by simple descriptions declaring some of them correct, while the other are treated as ungrammatical. The selection is based on socially relevant parameter. For English it is so called Standard English, the variant of English spoken by the upper middle-class. A variant of descriptive Grammars you know very well is so called practical Grammar designed mostly for foreigners. We shall not discuss any further different types of prescriptive Grammars since they are described in detail in the course of Methods of Teaching.
Grammatical descriptions aimed at understanding the Grammar of a language and because of that endeavouring to register the facts as accurate as possible are called descriptive Grammars. The main purpose of such Grammars is stating fact of a language. The idea of correctness is alien to these Grammars. If in some English dialect people use double negation or forms like "Us says", descriptive Grammars simply state the fact and try to explane it without any attempt to evaluate it from the point of view of "good" English. The forms of such Grammars may be different due to the variant of linguistic philosophy the author supports. Variants of descriptive Grammars are discussed in §§4-6. Descriptive Grammars usually include different interpretations of the fact registered in them. These interpretations present a third type of Grammars known as Theory of Grammar or theoretical Grammar. This course is predominantly interpretative and thus is its name "Theoretical Grammar of English".