A Major Difference Between Halliday's Model And Fawcett's

Halliday's model includes systems and structures on both strata of the content plane, whereas Fawcett's treats systems as semantics and structures as lexicogrammar. Halliday & Matthiessen (1999: 429):

In Fawcett’s model, there is only one system–structure cycle within the content plane: systems are interpreted as the semantics, linked through a “realisational component” to [content] form, which includes items and syntax, the latter being modelled structurally but not systemically; […] in our model there are two system-structure cycles, one in the semantics and one in the lexicogrammar. Terms in semantic systems are realised in semantic structures; and semantic systems and structures are in turn realised in lexicogrammatical ones.

The motivation for having two system–structure cycles is grammatical metaphor. Halliday & Matthiessen (1999: 429):

… grammatical metaphor is a central reason in our account for treating axis and stratification as independent dimensions, so that we have both semantic systems and structures and lexicogrammatical systems and structures. Since we [unlike Fawcett] allow for a stratification of content systems into semantics and lexicogrammar, we are in a stronger position to construe knowledge in terms of meaning. That is, the semantics can become more powerful and extensive if the lexicogrammar includes systems.