Conjunctive Adjuncts Vs Conjunctions

Halliday & Matthiessen (2004: 83-4):

… whereas conjunctions set up a grammatical (systemic–structural) relationship with another clause, which may be either preceding or following, the relationship established by conjunctive Adjuncts, while semantically cohesive, is not a structural one (hence they can relate only to what has gone before). These Adjuncts often are thematic; but they do not have to be.

Textual & Interpersonal Themes

Halliday & Matthiessen (2004: 83):

… the speaker or writer is making explicit the way the clause relates to the surrounding discourse (textual), or projecting his or her own angle on the value of what the clause is saying (interpersonal) …