There is no standard or orthodox type classification. Every type reference source reflects opinion and understanding of authors. Our classification is not an exception; don't be angry if you'll come to find out that it differs from other sources.
ParaType classification follows classical approach that mixes morphological, functional and historical classifications in one scale. That is why 'Serif' (which is morphological characteristic), 'Decorative' (which is functional) and 'Old Slavonic' (historical) listed as alternatives. Such an approach is not very scientific, but rather traditional and familiar to type users.