Context Vs Register

Halliday & Matthiessen (1999: 375):

Context is the ‘semiotic environment’ of language (and other socio-semiotic systems such as image systems); its systems specify what demands may be placed on language and what rôle it may play in responding to those demands.

Halliday & Matthiessen (1999: 563)

… a register is a particular probabilistic setting of the system; and the move from one register to another is a re-setting of these probabilities.