Vinay Jha wrote on what is astrology :

"Jyotiṣa is a Vedānga (an auxiliary text to the Vedas).  The first ever record for Jyotiṣa is found in the Veda. The earliest reference to Jyotiṣa as a vedānga is found in the Mundaka Upanishad and Chāndogya Upanishada also mentions it as a distinct discipline. The first Vedic Yajna in Yajurveda is Darsha-paurnamāsa Yajna, which needed correct timing of tithis (eg, New Moon or Darsha, and Full Moon or Poornamāsa). Vedas are concerned with Yajnas which can be performed only at astrologically auspicious moments."

Because early western writers on Hindu astrology did not have a background in Hinduism, and because they usually came from western astrology which is secular, they called the astrology from India eastern or Indian, or following BV Raman, Hindu astrology.  In India it was also called Jyotisha as Vinay Jha pointed out.   Several years ago, it became known as Vedic astrology, which ticked off many older western and even Indian astrologers, because they had not been told of the deep link between the hindu scriptures and ancient astrology.

Also, because the western system mostly resembles the Indian in the use of 9 planets, 12 signs, 12 houses along with aspects, the use of nakshatras or lunar mansions was seen as a separate distinct technique.  Now practitioners who delve deep in the deities of the 27 nakshatras see clearly that the myths, stories and lore for these deities is in fact, purely Vedic and Puranic.   Most of these mythical stories are found in the Rig-Veda which is one of the early Veda.  You cannot use the nakshatras and their incredibly rich depiction of deities without borrowing heavily from the Veda.

This has an importance in the use of period systems.   Most astrologers who know Indian astrology know that life is divided into periods, each ruled by a planet, in fact by up to 5 planets.   The best known system is Vimsottari Dasha.  It is based on the nakshatra, because the rulers used for the Dashas are planets associated with each nakshatra.   So when you work on prediction using Dashas, any Nakshatra Dasha, you are using nakshatras.  Nakshatras with their Deities are inherently Vedic as i explain next, and form the earliest astrological symbols.  They seem to be anterior to 12 sign astrological ideas, although this idea is purely based on the extant texts.

The nakshatras use many different categories of deities, planet rulers, and also many categories drawn directly from Shankhya philosophy, which is the philosophical system underlying the Upanishads and Bhagavad Gita, which are Vedic text.   

For instance the Doshas, Vata, Pitta, Kapha are in the Gita, it is part of Shankhya philosophy.  These link astrology with Ayurveda which is the Indian medicine.  The Gunas or 3 qualities are... a pure Shankhya concept, hence Vedic if you realize that most Vedic text are embeded with Shankhya philosophy.  The Tattvas or 5 Elements are given to each nakshatras and also each planet, this is a Shankhya concept.   In fact each category of Shankhya which means Number, and uses numbers to describe natural life as Prakriti, is seen in astrology.   

You could in fact say that there is more categories of symbols to the nakshatras than there are for the planets.   There are in fact more categories of symbols for nakshatras than there are for the signs, which are so crucial for both western and eastern astrology.  Nakshatras are a richer system in a way. 

There are many categories :  Guna, Gana, Elements, Goal, Gender, deities, planetary ruler, Animal, Shakti, Nature, along with the 10 or 11 kutas which are augmented with Vedha, Rajju, Shtree Deergha.   These kutas are used for mariage (or any relationship) work. 

The Vedic deities alone are so rich that they form the basic myths, motivations and karmic patterns seen in each nakshatra.   

Each deity is interlinked with other deities, for instance Agni the god of Fire is working with Indra the chief god or god of thunder, for the nakshatra Vishaka.  Bagha and Aryaman share duties for the 2 Phalgunies.  There are close relationships between Sravana and Dhanista and so forth. 

So at this point it is abundantly clear that calling the astrology of India Vedic astrology is totally in synch with its origin and use.  It has a strong foundation in Vedic lore and spirituality in being a limb of the Vedas, and it is said that Jyotisha formed part of the curriculum of the spiritual student in the ancient world, along with Yoga, Mathematic, Medicine, Ayurveda,meditation and prayer, and also knowledge of the Calendar (which is also astrological) or Panchanga.

Pierre Touchard 2023