In essence, Sanatan Dharma and Hinduism represent the vast principles, concepts, and philosophies that form the formless mold embodied in the organized religion we now call Hinduism. Old philosophically nuanced and present-day typically connotated religious system. This entailed differentiating between Sanatan Dharma and Hinduism, with origins, etymological definition, and philosophical review. 

Definitions and Etymology 

The term Sanatana Dharma is comes from the Sanskrit words meaning eternal way or eternal law. It has been referred to from time immemorial in ancient Hindu scriptures and is believed to be Much older than the term "Hinduism" by thousands of years. The Bhagavad-gita describes such:

"To deliver the pious and to annihilate the miscreants as well as to reestablish the principles of dharma, I advent Myself millennium after millennium." (Bhagavad Gita 4.8)

The origin of word Hinduism is  relatively closer to our present-day period and was given foreigners. It come from the Persian pronunciation of "Sindhu," which is the Indus River. It was used by foreigners to refer to the people living beyond the Indus River and their practices. It was the British colonial administrators who coined it as an official adjective for the religious sphere. 

Philosophical Basis

 Sanatan Dharma is the philosophical informational structure and timeless principles from which arose Hinduism. The Chandogya Upanishad expresses this eternal nature:
"That which exists is One; though the sages call it by various names." (Chandogya Upanishad 6.2.1) Modern Hinduism is now seen as the cultural and religious expression of the principles of Sanatan Dharma as they evolve in the region over the period of time   It embraces the plethora of practices, deities, and philosophies under one name.

Scope and Practice 

Sanatan Dharma postulates universal spiritual laws that are applicable to all souls regardless of their religion and culture. It’s core are dharma (Being righteous), karma (action and consequence), and moksha (liberation or slavation). The Brihadaranyaka Upanishad states:

"You are what your deepest desire is. As is your desire, so is your intention. As is your intention, so is your will. As is your will, so is your deed. As is your deed, so is your destiny.”
" (Brihadaranyaka Upanishad 4.4.5)

Hinduism refers for the specific cultural, ritual, and social practices that developed over the years in the Indian civilization. These include worshiping in temples, festivals and institutions like caste are not inherent part of core Sanatan Dharma's .

Historical Evolution 

Sanatan Dharm- an uninterrupted spiritual tradition that can be traced continuously back to the Vedic period (1500-500 BCE). The Rig Veda, one of the oldest surviving texts in religious history of mankind, says the following: "Truth is one, the wise call it by many names." (Rig Veda 1.164.46)

Hinduism is how these ancient truths expressed themselves under varying historical conditions, subject to foreign invasions, cultural invasions, and social reform over the length and breadth of Indian history.  

Contemporary Relevance 

Understanding this distinction presents those following this tradition in the present-day light of separating eternal principles from culturally determined practices. 

The historian Sarvepalli Radhakrishnan rightly stated that: "Hinduism is not just a belief. It is the union of reason and intuition that cannot be defined but is only to be experienced." 

CONCLUSION 

To sum up, while Sanatan Dharma is the eternal and unchanging spiritual laws that transcend time and culture, Hinduism represents the many possible ways in which these laws were manifested within Indian civilization. For some trying to embrace this tradition, this perception will help them appreciate both the ageless wisdom and the vibrant culture that has developed around it.

By accepting Sanatan Dharma as the philosophy and Hinduism as its expression, a seeker would better understand this great spiritual tradition, through embracing its universal truths, acknowledge its varied expressions.