The four terms you are asking about—transformational-generative grammar, comparative-historical grammar, traditional grammar, and structural grammar—are actually four distinct theories or schools of thought about language. They are far too advanced to be discussed with sufficient rigor here. From a layperson’s standpoint, however, we can get a general idea of their differences by starting with the more familiar theory and proceeding to the unfamiliar or more complex ones.
Traditional grammar is the prescriptive approach to language that’s normally taught in English-language schools from kinder to college; it is, of course, also the grammar used by the English-language mass media and books as well as the primary basis for the discussions of proper and improper English usage in this Forum. The prescriptive rules and concepts used by traditional grammar are primarily based on Latin grammar, and in the case of the English used in the Philippines, traditional grammar follows the American English standard.
Structural grammar is a descriptive approach to linguistics that focuses on the mechanics and construction of sentences. It is more concerned with how the sentence itself is constructed rather than with the implications of individual words. This structural approach, which is the basis for the creation of most written documents, assumes that what is seen on the surface is also the straightforward meaning behind the words of the sentence.
Comparative-historical grammar is an approach to linguistics that seeks to establish an explanation for the relationships between languages, and it’s one that assumes that linguistic change is largely systematic and rule-based. Early work in this linguistics approach focused on relationships between languages and groups of languages primarily in terms of a common ancestry or the same root-language.
Transformational generative grammar, a relatively new theory of linguistics popularized by Noam Chomsky in the 1950s, postulates that all languages have the same deep structure, but that their respective surface structures differ because of the application of different rules for transformations, pronunciation, and word insertion. This theory asserts that when words and pronunciations are added to the surface structure of a particular language, what emerges is identical to an actual sentence in that language.
These are only bare-bones, nonspecialist descriptions of the four linguistic terms you listed, and they focus primarily on the characteristics that can best distinguish them from one another. A deeper study of linguistics is needed for a fuller understanding and appreciation of the theories of language behind these terms.
