Halliday & Matthiessen (2014: 320):
Circumstances of Degree shade into mood Adjuncts of intensity. The difference between them can be seen in an example such as it almost destroyed the house:(Degree) ‘it destroyed the house to a large extent’,
(Mood Ajunct) ‘it didn’t destroy the house’.
Circumstances of Degree construe the extent to which the process is actualised, and are thus agnate with lexical grading, as is seen particularly clearly in the lexicogrammar of emotion (cf. adore ‘love deeply’; detest ‘dislike intensely’). In contrast, Adjuncts of intensity assess the proposition – how close it comes to being actualised, and are thus agnate with other types of assessment and related to polarity.