There is so much confusion in your post sir
I don't want to go into some theology based discussion, as it takes a unnecessary route here. Fact of the matter is that, Buddhism/Jainism themselves are off shoots of the so called larger 'hindu fold'. Another fact to keep in mind is that, if one goes into deep study -- there is no Hindu religion as such. It's a conglomerate of beliefs / customs / theological discussions / interpretations of few texts like Vedas and puranas which then got included into daily lives by people of this land. None of these remained stagnant, as in they kept evolving and spreading and localizing within sub continent region. Newer belief systems disrupted but then also got localized here. In a very macro sense is what am talking here
The word Hindu or Hinduism is something outsiders gave to the subcontinent on a whole, as even today people struggle to grasp the variety of beliefs and thoughts in this large land. One personality is celebrated in one part, and the same vilified in other. There is no black and white, it's all shades of grey.
In short it's the same people here (call them people who followed Dharmic/Vedic traditions or Hindu customs if we used the word given by outsiders for people living on the other side of Sindhu river valley) in this land, who were influenced in physical and mental ways by insiders and outsiders. So if we go really technical and use the correct word, the Dharmic people have by and large remained in this land (right from present day Pakistan to Kanyakumari, it just evolved over time.. I mean people's beliefs customs etc, but then some kind of basic thoughts or beliefs permeate the larger way of living, which makes one wonder why there are subtle similarities in few things between present day Hindus Muslims Christians etc.)
That's why you know Indians are full of shit. Never trust a brown person with your spirituality 
