The orthodox schools were:
(1) Nyāya
(2) Vaiśeṣika
(3) Sāṅkhya
(4) Yoga
(5) Mīmāṃsā
(6) Vedanta (also called Uttara Mimāṃsā)
Inasmuch as these groups all acknowledge the authority of the Vedas, they were part of the Hindu tradition.
They all took form at the end of the Vedic period, when Buddhism and Jainism were also developing (6th century BCE). In the following centuries, philosophers in these schools continued to add their ideas to these traditions.