From the texts it appears that there is a deep connection between Parvati and Durga and generally we believe that the former has emerged from the latter. However Devi Bhagwat Puran Chapter 28 of Book 7 gives the account of Parvati transforming into Shatakshi and then Shakambhari who was renamed Durga after she killed the demon Durgam:
There, Goddess Parvati went to Himalayas where Gods were praying to her. Gods informed her about the drought condition over the earth. Seeing the dreadful condition of the earth, she created innumerable eyes within Her body and became visible. That Upholder of the Universe, showed Her form and began to shed waters from Her eyes. For nine nights continuously, the heavy rains poured down out of the waters flowing from Her eyes. Seeing the misery of all the people, out of pity, She showered incessantly tears from Her eyes; and all the people and medicines were satisfied. What more than this, out of those tears, the rivers began to flow. The Gods that remained hidden in the mountain caves, now came out. Then the sages, united with the Gods, began to praise and sing hymns to the Goddess. Then, Shatakshi Devi transformed her appearance into a wonderful form, her eight hands held foods like grains, cereals, vegetables, greens, fruits, meat and other herbs, she wore a beautiful garment, this new form of Goddess is known as Shakambhari. Goddess Parvati transformed her appearance. Now she looked ferocious in her new appearance. She was well equipped with all sorts of lethal weapons and was mounted on a lion. She thundered loudly and challenged Durgamasur.
69-73. The Devas said :-- “O Auspicious One! Thou art the only Cause of this Illusion of this world, presenting an unreal appearance. So Thou art the Lady of all the beings. So, Obeisance to Thee, the S’âkambharî! Hundred-eyed! O Auspicious One! Thou art sung in all the Upanisadas; The Destroyer of the Durgama Asura! We bow down to Thee, the Lord of Mâyâ, the Dweller in the five sheaths Anna, Rasa, etc. We meditate upon Thee, the Lady of the universe, as demonstrated by Pranava Aum, whom the chief Munis meditate with their Nirvikalpa hearts. Thou art the Mother of the endless crores of universe! Thou assumest the Divine Bodies at times for our welfare! Thou art the Mother of Brahmâ, Visnu and others; we bow down to Thee with all our heart.
74-80. Vyâsa said :-- O King! Thus when Brahmâ, Visnu, Hara and the other Devas praised and chanted various hymns to the Devî and worshipped Her with various excellent articles, She became instantly pleased. Then the Devî, graciously pleased, handed over the Vedas to the Brâhmanas. At last, She, the Cuckoo-voiced, made a special address to them. “These Vedas are the excellent parts of My body. So preserve these with your greatest care. The more so, when you all have seen with your own eyes what a great calamity befell on you when these Vedas went away out of your hands! You should all worship and serve Me (the Controller of the Space) always; there is no other thing higher than this that I can advise you for your welfare. Read always these My excellent glorious deeds. I will be pleased thereby and will destroy all your bad calamities and misfortunes. My name is Durgâ, because I have killed this demon Durgama; so he, who will take My name Durgâ and S’atâksî, he will be able to unveil my Mâyâ and walk freely. No use in telling more than this that I tell you now, O Devas, the Essence of all essences :-- Both the Suras and the Asuras would always serve Me and Me, alone.”
So going by this account, Durga is Parvati returning to her original form rather than an incarnation.