Skythians / Sakia Saka Sakyans (different ways to write it in English), and Sarmatians and Taurian Tavry - are synonyms for the same indo-european (arian) ethnicity scattered on a vast territory, and therefore living under different names in space and history. Of course they were a bit mixed with other ethnicities in the bordering regions, sometimes with other indo-european tribes or non-indo european.
Buddha Sakia muni was no doubt a Wiseman of the Saki tribe, because the whole Buddhist knowledge and scripts is using sanskrit/ arian words immensely close to slavic languages. Sanskrit is the closest to sanskrit among the whole indo-european family of languages. Buddha comes from budit'(see sansrit and Russian or any slavic language) to wake up - the awake one. When indian sanskritologists come to Russian villages, they do not need translator.
Buddha's tribe was just one of the aryan tribes that migrated down to India. In Vedas there are scriptures describing where they came from. Many river names or places are still in the north of Russia. Vedas is a Sanskrit and Russian Word for Knowledge. The words wissen or wisdom all come from the word vedat, meaning "to know". The words knowledge, cognition, kenntniss and znat (from russian) are words of the same root. Every linguist knows it.
Ayurveda is the folk modification of the word aryaveda - arian knowledge. That is why the most ancient and well known clinic of ayurveda in Kottakkal has the name Arya Vaidya Sala, and not Ayurveda Sala.
Every indian knows that aryans came from the north to Industan. They were tall white-skinned blonds with blue eyes, and they brought the Vedas to Hindustan. Every linguist and also every genetic specialists knows about the split of the R1 haplogroup 4500 years BC. That's when this single ethnicity of protoindoeuropeans (=aryans) got split in the north of Russia, and started migrating in different directions to the West to form the west European tribes (Celtic, Germanic, Romanic, ancestors of some Greeks tribes, or R1B haplogroup today).
The second haplogroup R1a are protoslavic tribes which are the same ethnicity known under the names as follows: Taurian, (Th)Frakian, Skythian, Sakian, and Sarmatian (migrated to spread and settle from Elba (Laba) to Japan). Some of their tribes spread further southwards to India and also to the Arabic world to Egypt, and even reached China. That's why Pharaos had blue eyes and belonged to R1a. Persians of aryan type are also R1a. That's where the world Iran comes from. Pharsi is an indo-european language. In Tibet and China there are not only excavations with R1a mummified bodies of ancient tribes, but also the cultural symbolism and texts hold many traces.
Protoindoeuropeans or Aryans everywhere spread their knowledge with them and the lifestyle where ever it matched. Tibetan Buddhist Tantra (Journey to Daikini Land) says it was inherited from Ishvara- That is Shiva or Siva or Svarog or Zeus, or Jahveh or Saboath, Savaof or Sevas- an Aryan name for God.
The protoindoeuropean tribes R1 split into R1a and R1b split and started their migration downwards from the North of Russia most probably due to the climate change. Buddha Sakia Muni was just one of them. Saki or Sakian word for scythian (ancient slavic or Russian) ancestry places and culture is known for example in the Crimea (Tavrida) - Saki - Lake for example. The same tribes you see in the North of Pakistan, or Afganistan, Kashmir, Tajikistan.
If you travel from China to Pakistan you will see plenty of white European blue-eyed and blond or fair-hair people. Looking absolutely Russian. Their language is indoeuropean, close to Russian. You will confuse them with slavic looking Russians and they will take slavic looking Russians travelling there for their own, if they get dressed typical of these places. These tribes have million different names there. But it is the same ethnicity with some linguistic and of course cultural modifications throughout history. But everywhere you find the same main elements.