Taxis Vs Embedding

Halliday & Matthiessen (2004: 426):

It is important to distinguish between the 'tactic' relations of parataxis and hypotaxis on the one hand and embedding on the other.  Whereas parataxis and hypotaxis are relations between clauses (or other ranking elements), embedding is not.  Embedding is a semogenic mechanism whereby a clause or phrase comes to function as a constituent within the structure of a group, which itself is a constituent of a clause … .  The embedded clause functions in the structure of the group, and the group functions in the structure of the clause.

The distinction between hypotactic and embedded expansions is set out in Halliday & Matthiessen (2004: 442) in Table 7(15).