The commentary makes a subtle distinction: both generic al- (لام الحقيقة) and mental reference (العهد الذهني) may involve a nature available to the mind. The difference is whether attention rests on that nature as such, or evokes a suitable possible instance under it.
Examples:
«الإِنْسَانُ حَيَوَانٌ نَاطِقٌ» — “Human is a rational animal,” a definition concerning the human kind.
«اُدْخُلِ السُّوقَ» — “Enter the market,” referring to a practical instance of a familiar type.
These are useful contrasts, but the source examines alternative terminology and arguments about the precise relationship between the usages. The distinction should not be turned into an inflexible mechanical rule for every sentence.