Maa Katyayani is the form of Durgadevi. She is one of the Navadurgas. As per the Devi Mahatmya, the devatas, frustrated by the nuisance caused by Mahishasura, approached Lord Vishnu, Lord Brahma, and Lord Shiva; at that time, the trio was very angry. Not only they, but even the other devatas were also angry. From their anger came a light from their bodies and merged into one big light, forming a Devi. Different devatas gave weapons to Devi.
At that time, Shiva gave one trishula from His trishula; Lord Vishnu gave His Chakra; Lord Brahma gave the japamaala and the kamandalu to Devi. Vayudeva gave a bow and arrow to Devi; Yama gave Kaaladanda to Devi; Indra gave His vajra to Devi; Varunadeva gave Paasha to Devi; Kaala gave Her a sword and a shield; Vishvakarma gave Her the axe; and like this all the devatas gave Her their weapons from their own weapons, ornaments, etc.
Actually, these lights which came from the devatas are Devi’s roopas. As we say, ‘Yaa devi sarvabhooteshu shaktiroopena samsthita…’ So, in the devatas She is present in the form of their powers, or Shakti, or even their ability to do work. But within Vishnu, She is not present as Shakti, but that Shakti itself is under Lord Vishnu, as per the Ambhruni Sukta, which says, ‘Aham suve pitaramasya moordhan mama yonirapsvantha samudre…’ which means Devi can do the creation, sustenance, and even the destruction of the universe, and Brahma and Rudra too obtain their positions due to Devi’s blessings, but the source of this immense power of Devi is the one who sleeps in the samudra/ksheerasamudra, which is Lord Vishnu. Plus, She is Vishnumaaya, which means She is Vishnu’s Maya.
Even in the weapons too, it is She who is present as the Shakti within those weapons. That’s why we worship Devi in the tools we use daily during Aayudha Pooja. Now, coming to the point, after all this, Devi goes to Sage Kaatyaayana’s hermitage and accepts His pooja. Another light came from Sage Kaatyayana too, in which Devi was present as Shaktiroopini within him, and merged into the Devi. That’s why, since in one form She came from Sage Kaatyayana, She is known as Kaatyaayani Devi. So, She is Durgadevi only.
Now, coming to why She is worshipped on Navaratri Day 6? The reason is simple. As per the Devi Kavacha, which comes in the Devi Mahatmya of the Markandeya Purana, Lord Brahma tells Narada that there are 9 forms of Durga. First is Shailaputri, second is Brahmacharini, third is Chandraghanta, and fourth is Kushmaanda. The fifth one is Skandamaata, and the sixth one is Kaatyaayani. The seventh one is Kaalaraatri, and the eighth is Mahagouri. The ninth one is Siddhidaatri. Some people even call Siddhidaatri, as Devadooti. Like this, there are nine Durgas. These nine Durgas are worshipped individually in the 9 days of Navaratri. Like that, today is the 6th day of Navaratri, and hence, Maa Kaatyaayani is worshipped today.
Both Lakshmidevi’s Durgaroopa and Umadevi’s Durgaroopa are known by the name Katyayani. The Gopikas also did the Katyayani Vrata to obtain Krishna as their husband. So, tomorrow Kaalaratri Devi is worshipped.
Hope this helps!
Jay SriRam!
ShriMahakaali Mahalakshmi Mahasarasvatyatmike SriChandika Durgaantargata ShriKrishnarpanamastu!