[...] the difference between the two is a difference of kind, rather than just one of degree. If we use maximal bracketing, we are taking the concept of bracketing as a powerful explanatory device; in other words, we are attempting to explain as much of grammar as possibile in terms of constituent structure [...] If we use minimal bracketing, we are relegating the concept of bracketing to a less important role, requiring the notion of constituency to take us only a limited way in the explanation of the grammar, and no further. This means, of course, that we have to bring in other concepts to take over the burden of interpretation where constituent structure is no longer relevant. The concepts in question are, in the first instance, functional ones.
- Halliday (1985), a pag.24-25

Maximal bracketing is a statement of the 'order of composition' of the constituent parts. It expresses the idea that some constructions are more closely bonded than others, to the extent that, given any grammatical structure, it is possible to specify the order in which all the pieces are put together, pair by pair. So for example in 2-9 (c) the meaning is ʻto form the construction 'tigers climb trees', first put together 'climb' + 'trees' then put together 'tigers' + 'climb trees'.ʼ It says nothing about the function that any of the pieces have in any construction; in fact it does not imply that they have any fuction at all.
- Halliday (1985), a pag.26