Most of you may be familiar with the list of "common errors" in school grammar, like: the man whom I saw, but not: the man who I saw.
For most of its long history the study of language has been prescriptive, which means that its purpose has been to tell people what they should say or write. As learners of English, you may be familiar with Bo Bin English Grammar, which is quite prescriptive.
Descriptive linguistics, on the other hand, aims to record objectively what people do say or write without commenting on which is the "correct" way. Descriptive linguists pay attention to the whole of a language, in contrast to the selective coverage of more traditional prescriptive approaches.
Advances in computer technology have facilitated great progress in corpus linguistics, which involves the computational analysis of vast collections of textual data. This makes descriptive linguists work more fruitful.
Corpus linguistics has the capacity for providing powerful challenges to common assumptions about linguistic phenomena, enabling the analyst to discuss such issues as frequency of occurrence and patterns of collocation of items whose relationship is not transparent to intuition.
One of the best known products of computer-stored corpus work is the descriptive reference grammar of Quirk and his colleagues (Quirk et al, 1972; 1985) and its various spinoffs.
We try to talk about language by using language—that's why we need a METALANGUAGE. Any science is like that. Terminology is part of the study but we hope you will not get stuck by it. When you read, try to guess the meaning first, and then you may go to the glossary for a quick look.
How about different schools? Different schools enrich our understanding of language from different perspectives. For example, FUNCTIONAL LINGUISTs believe that the search of the FORMAL LINGUISTs like Chomsky for an autonomous linguistics, with the goal of describing the idealized competence of an idealized speaker is not plausible, nor was the earlier effort of STRUCTURAL LINGUISTs to account for language structure without taking meaning into account. But formalists are still working hard in the belief that their job will contribute significantly to our understanding of the human mind.
As Ronald Carter puts it,
The fact that there is a dominant paradigm in linguistics should not and does not preclude the existence of other paradigms in theory and practice. For example, SYSTEMIC-FUNCTIONAL MODELs of language description such as those developed by or under the influence of Halliday have a more socio-linguistic focus, accounting for contextual variation and working often from data which is naturally-occurring rather than data which is invented. (Ronald Carter "Discourse Literacy" in Allison, 1998: 9)
For the time being, as learners it is wise for you to ignore the academic sound and fury and focus on the general picture of language studies, as all schools will agree about something in general and that is what we are presenting here. When it comes to difference, put a question mark which will lead to your further pursuit.