Context Vs Cotext

Halliday (2007 [1991]: 271):

Originally, the context meant the accompanying text, the wording that came before and after whatever was under attention. In the nineteenth century it was extended to things other than language, both concrete and abstract: the context of the building, the moral context of the day; but if you were talking about language, then it still referred to the surrounding words, and it was only in modern linguistics that it came to refer to the non-verbal environment in which language was used. When that had happened, it was Catford, I think, who suggested that we now needed another term to refer explicitly to the verbal environment; and he proposed the term “co-text”.

For the difference between material setting, context and co-text, click here.
For material setting vs context see here.

Context Of Situation Vs Setting

Halliday (2007 [1991]: 278):

The setting, on the other hand, is the immediate material environment. This may be a direct manifestation of the context of situation, and so be integrated into it: if the situation is one of, say, medical care, involving a doctor and one or more patients, then the setting of hospital or clinic is a relevant part of the picture. But even there the setting does not constitute the context of situation …

Martin’s Cline Of Instantiation Applied To Martin’s Stratification

Martin's stratification: 

genre, register, discourse semantics, lexicogrammar, phonology

Martin's cline of instantiation: 

system, genre/register, text type, text, reading.

On this model,

(A)

(1) genre is simultaneously more abstract than register (in terms of stratification), and a sub-potential of register (in terms of the latter stratum's instantiation) — which is logically incoherent;

(2) register is simultaneously more abstract than discourse semantics (in terms of stratification) and a sub-potential of discourse semantics (in terms of the latter stratum's instantiation) — which is logically incoherent;

(B)

(1) genre is simultaneously a stratal system and a sub-potential of itself (in terms of that stratum's instantiation) — which is logically incoherent;

(2) register is simultaneously a stratal system and a sub-potential of itself (in terms of that stratum's instantiation) — which is logically incoherent;

etc …

Register & Context 2012: Christian Matthiessen Part 2

Register & Context 2012: Christian Matthiessen Part 1