Samkhya, Nyaya, or Vaiseshika are all a form of gnosticism applied on the Vedic religion, they are not truly Vedic, even though they hold the Vedas in respect as a scripture of knowledge. They believe God doesn’t create matter unlike the Vedic religion. They do share similar ethics to Vedic religions however.
Yoga really isn’t a philosophy on its own, its usually just grouped along other philosophies (such as Samkhya or Vedanta).
These 5 are the Astika schools of Indian philosophy, which holds the Vedas as a means of knowledge. The rest that don’t are the Nastika:
Charvaka and Ajivika may not be categorised as Hindu. They are Atheistic which is entirely against Vedanta. Charvaka is even hedonistic (against Dharma). Ajivika is deterministic & fatalistic (also adharmic).
Buddhism is atheistic but follows similar Dharma to the Vedic religions. Of course it’s Atheism is against Vedanta, & Buddhists dont hold the Vedas as a source of knowledge, but the outcomes and ethics of this religion are still similar to the Vedic religion.
Jainism is also Atheistic, but unlike Buddhism, it believes in the existence of souls (& unlike Vedanta or Samkhya these souls are independent). They also have similar ethical views to both Buddhism or Hinduism. Though they do take pacifism to its extreme.
The classification of Indian philosophies based on their acceptance of the Vedas is valid, as it distinguishes Astika from Nastika traditions.
However, While these classifications are useful, they oversimplify the diversity within Indian philosophical tr