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If the question is about Hinduism at present, then I think it is faulty. Of the six Astika schools—Sankya, Yoga, Nyaya, Vaisheshika, Mimangsha, Vedanta, each which differed a little bit in their philosophy—are all dead except the Vedanta. Hence, Upanishad means Vedanta now. Later, various philosophies emerged from Vedanta, namely Advaita, Bishista advaita, ...


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There is a different way of classification within Asktika i.e. those who accept the authority of vedas. Astikas can be classified into 2 groups: Vedanta / YogaVedanta, all the schools (including vedanta) mentioned in the question above fall under this category. VedaAgama / Agama: ShaivaAgamas(Shiva), ViashnAgamas(Vishnu), ShaktAgamas(Shakti) (maybe more) ...


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