Hasan uses 'social' to refer to parameters that classify language users in terms of age, gender, class, ethnicity, etc. Such parameters are relevant to both tenor, the interpersonal dimension of context (the culture as semiotic system) — not register — and the semantic variation that correlates with social difference.
Halliday's use of 'social' as an order of complexity refers to the social systems like those of eusocial insects (ants, bees, termites), which are organised on the basis of value, not semiosis.
Halliday's notion of language as a 'social semiotic' distinguishes language from other semiotic systems that are not social, such as the perceptual systems of the brain, as described by Gerald Edelman.
