Halliday & Matthiessen (2014: 293):
The line between ‘attributive’ and ‘identifying’ modes is less clear in the ‘circumstantial’ than in the ‘intensive’ type of ‘relational’ clause. This is natural, since it is less obvious whether an expression such as on the mat designates a class (that has members — the class of things on the mat) or an identity (the thing that is identified by being on the mat). Nevertheless there is a distinction …