To understand Hinduism, one needs to distinguish between three different concepts: Worldview, philosophy, and religion.
1. Worldview (or Weltanschauung) is a set of beliefs. The Vedic worldview or the worldview of the Sarasvati-Indus civilization is commonly referred to as Hinduism or Sanātana Dharma. Swami Vivekananda suggested that we should not use the word 'Hindu,' but instead use the word 'Vaidika' (follower of the Vedas), to convey the meaning unambiguously (Complete Works, Volume 3, Page 118). The Vedas are called Śruti, “that which has been directly heard.” Vedas consist of Saṁhitās, Brāhmaṇas, Āraṇyakas, and Upanishads. Hinduism or the Vedic worldview is characterized by four fundamental beliefs. All those, and only those, who have these beliefs are Vaidikas or Hindus, irrespective of where and to whom they were born.
(i). The first belief is in the existence of the Ātman, our real self, pure and untouched by our physical body and subtle body (that includes mind, intellect, citta and ahaṅkāra). When the physical body dies, the subtle body takes on another physical body.
(ii). The second belief is in the law of karma: all actions ordain for their doers joy or sorrow in the future depending on whether the action is good or bad. Often, individuals are required to take birth in another body to experience the joy or suffering that is due to them because of their past actions.
(iii). The third belief is about moksha, release from the cycle of birth and death: if we could be free of all desires that lead us to selfish action, there would be no fuel to propel us into another birth and we would be free (S. Dasgupta, "A history of Indian philosophy," Vol 1, Page 71).
(iv). The fourth belief is accepting that all the various paths taken by different people towards moksha are valid and true. People are at different levels because of their past baggage, and hence any one specific path cannot suit everyone. Swami Vivekananda said: "India alone was to be, of all lands, the land of toleration and of spirituality... For one of the greatest sages that was ever born found out here in India even at that distant time, which history cannot reach, and into whose gloom even tradition itself dares not peep — in that distant time the sage arose and declared, — 'He who exists is one; the sages call Him variously.' This is one of the most memorable sentences that was ever uttered, one of the grandest truths that was ever discovered. And for us Hindus this truth has been the very backbone of our national existence. For throughout the vistas of the centuries of our national life, this one idea comes down, gaining in volume and in fullness till it has permeated the whole of our national existence, till it has mingled in our blood, and has become one with us. We live that grand truth in every vein, and our country has become the glorious land of toleration" (Complete Works, Volume 3, Pages 186-187)
2. When the different beliefs of a Weltanschauung are systematized and put into a coherent framework, it is philosophy. The worldview may have beliefs that are inconsistent with each other, but philosophy links the beliefs in a logically consistent manner. The schools of Indian philosophy fall into two main divisions according as they do or do not accept the authority of the Vedas: nāstika (not believing in the Vedas) and āstika (believing in the Vedas). The āstika schools regard the Vedas as recording the transcendental experience of the first mighty seers. This experience cannot and should not contradict similar experience in any age or country. Six major āstika schools of philosophy systematize the Vedic worldview or the Hinduism Weltanschauung. They are Nyāya, Vaiśeṣika, Sāṁkhya, Yoga, Pūrva Mīmāṁsā, and Vedānta.
3. Religion is a practical means of trying to attain moksha, often through service or worship. It is generally seen as pūjā (worship) of iṣṭa (chosen deity) or a personal God. Six major clusters of religions (Ṣaṇmata) that subscribe to the Hinduism Weltanschauung or Vedic worldview are Vaishnavism (Vishnu), Shaivism (Shiva), Shāktam (Shakti), Gāṇāpatyam (Gaṇeśa), Skāndam/Kaumāram (Kārtikeya), Sauryam (Sūrya). Each of these has its own rituals, methods of worship, etc. Like the worldview, religion is also not by birth. For example, how can we call someone a Shiva-worshipper or a Shaivite if she does not worship Shiva, though her parents may be Shiva-worshippers or Shaivites? All those, and only those, who worship Shiva are Shiva-worshippers or Shaivites, irrespective of where and to whom they were born.
Accepting all religions as true and valid is a unique aspect of Vedic worldview or Hinduism, making it difficult for most people to understand Hinduism and Vaidika religions.