Halliday & Matthiessen (2014: 369-70):
The two different number systems operating with specific and non-specific determination apply to all nominal groups, but the typical range of determiners and the semantic patterns of agnation depend on whether a given nominal group refers to
(i) a member or members of a class (particular reference) or to
(ii) to a class to which members belong (general, or ‘generic’, reference): see Table 6-7.
Note that this is 'reference' in the sense of ideational denotation, not in the sense of cohesion — nominal groups don't refer in the cohesive sense. Matthiessen here risks imparting the same confusion found in Martin's (1992) model of IDENTIFICATION (reference as semantic choice).