Who is Ambika
As per Shiva Purana, the advent of the Samsara owes its origin to the craving of the absolute to multiply in many. Sadashiva, the Param Brahman, had created Shakti out of his own form as an autonomous entity, else she would never part with him. She was Ambika, not Sati or Parvati, as often believed. She is also known as Prakruti, Sarveshwari, Nitya and sometimes as Jagdamba. She is portrayed as having eight arms.
Who is Durga
In the clan of Hiranyaksha, there was a Daitya called Durgamasura. He was son of Ruru. Durgamasura had invaded Amrawati, the capital city of Indra, and captured it from Devas. Exiled from home, Devas then worshipped Ambika to gather strength. When Durgamasura came to know about it, he this time declared war on Dura. A furious battle ensued where Durga demolished all the forces of Durgamasura. After this Ambika came to be known as Durga, the warrior Goddess, who is at the center of Navratri festivities.
Who is Sati
Shiva was wedded to Dakshayini, the daughter of King Daksha. She is also called Sati. After having seen her husband being humiliated, she left her mortal form by jumping in the fire pit of Yajna which was being performed by Daksha. Shiva carried her mutilated body on his shoulders and where her body parts fell, there is now a Shaki Pith, total 52 of them, dotted across India. She was reborn as Parvati and eventually got married to Shiva again after a rigorous Tapasya to appease him. Parvati is also called Gauri and Mahagauri. The “Shera waali” (one who rides a lion) and “Pahado waali” (one who resides in mountains) are adulations for Parvati, often confused for Durga.
Who are Navdurga
Shailputri, Brahamacharini, Chandraghanta, Kushmanda, Skandmaata, Katyayini, Kalratri, Mahaguari and Siddhidatri : These are Navdurga, the nine forms of Durga, who are worshipped during the course of nine day and nights of Navratri. Shailputri is one of the names of Parvati, which literally means : “Daughter of the mountains.” She got the name of Brahamacharini for rigorously worshipping Shiva to attain him. Chandraghanta means one who bears moon on her head, just like Shiva. One who contains all of Brahmanda or Universe is called Kushmanda. Being the mother of Skand (Kartikeya) gave her the name of Skandmata. Being the daughter of Maharishi Katyayana gave her the name of Katyayini. Her fair complexion gave her the name of Mahagauri. Similarly, names like Siddhidatri and Kalratri describe her various forms as one who provides with Siddhi and one who can solve all troubles.