From your source: "Hinduism is often referred to as Sanātana Dharma, a Sanskrit phrase meaning 'the eternal law,' by its adherents." The term "Hindu" is misleading (that's another story). But yes, sometimes the term "
Sanatana Dharma" is used to designate the religion. At other times, it is used to describe a set of religious concepts.
Some observers would argue that Buddhism is just one aspect of an increasingly diversified S
anatana Dharma. The Jain and Sihk religions being two additional strands of the same basic root concepts. Buddhism was more widespread (geographically) and made its way all the way to China and Japan.
Although some Buddhist teachings are clearly attempts to set it apart from the old Hindu culture, the spread of Buddhism did not supercede Hinduism, nor was it an attempt to make Hinduism obsolete. It seems Hindu-Buddhist culture was actually the norm in some parts of the world for hundreds of years. (Similarly, early Christians were Jews first and Jesus evidently saw himself as a Jew who was trying to refine/extend the existing Judaic religion, not introduce something new that would supercede it.)
Regarding Buddhism, one might argue that it's not really a doctrine at all, but rather a set of practices. So to compare Buddhism and Hinduism as though they are different religions can be tricky.
Anyway, here's an interesting taker on it:
Buddhist scholar, Mr. Jing-Wuou-Yang gave a speech at Nanjing Nor mal University in China, entitled “Buddhism is neither a Religion nor a Philosophy, but the Essential for our modern time.” He says, “Buddhism is a most virtuous and perfect education based on Sanatana Traditions of India.”
Source:
Buddhism: Education of Sanatan dharma (Part I & II)
In the article it is suggested that to speak in terms if the so-called "Buddhist period" in India's history is misleading because there was never any real operational distinction between Buddhism and Hinduism. Even so-called "Buddhist deities" are hard to distinguish from what was described in the old Indian religion.
What we Westerners think of as Buddhism today is a mixture of Chinese and Japanese folk religions plus a select set of "Hindu" concepts and practices.
