An ELT Glossary : Language Systems

The four language systems are :

a) Grammar  :  This deals with how the morphemes in a language combine into acceptable structure with recognisable meaning. For example:  John starts work on Monday can be analysed into  parts such as subject + verb + object + adverbial; the verb can be analysed into component morphemes such as base form + 3rd person s; the adverbial can be analysed into components such as preposition + proper noun.

b) Lexis : This deals with the words in the language and their meanings. For example, what are the similarities and differences between the words thin, slim, scrawny, lanky, slender, and emaciated.

c) Phonology (also called Phonemics) : This deals with the sounds of a language, how they combine into meaningful units, how they may be affected by neighbouring sounds in connected speech, and how stress and intonation may contribute to the meaning of words or utterance

d) Discourse :  the study of language in use in extended texts (whether written or spoken). Eg discourse analysis would seek to explain why the sequence ...

A :  The phone's ringing!
B :  I'm on Skype
A :  I'm in the bath!

... is comprehensible as a request, a refusal of a request plus a further request, and a refusal of that request -  even though there is nothing in the language itself to indicate it.