Vedic vs Hindu

Hindu is more of a cultural term than a religious term. It was originally used by the Persians to refer to people with similar cultural values, even if they practiced different religions. To this day, Indian law often says Hindu when it actually means religions that originated in India.

Thus, if you want to talk about cultural values — such as yoga, dharma, karma, chakra, yuga, nirvana, ahimsa etc you want to refer to it as Hindu — as these cultural values are common to many Indian religions. If you want to be more politically correct, you can use the word dharmic — all major Indian religions are based on dharmic values. You can also use Hindu when you talk of Indian epics — Ramayana, Mahabharata etc — these are also common across India’s religions, languages and belief systems.

You want to use Vedic when you are referring to one particular Indian religion/belief system. It is one of the dominant ones in India, but not the only belief system in “Hinduism”.

The Vedas are a corpus of finest and most respected of the Indian texts that are often divided into 4 books — Rig, Yajur, Sama, Atharva. They are primarily centered on rituals. Each of these books have different parts — Samhita [mantras], Aranyaka[experiments and ceremonies], Brahmana [commentary] and Upanishads[philosophy].

Connected to these are 6 Vedangas [studies of grammar, poetry, astrology etc], 4 Upavedas [study of archery, medicine, music and architecture] and Vedanta [a school of philosophy].

If you are talking about these particular things, then you want to refer to it as Vedic. We often refer to scholars and priests whose career is made around study of Vedas as Vedic.

If you want to use other aspects of Indian culture then use the word Hindu, which in the past was the synonym for Indian.