According to Shakta traditions, Adi Shakti exists before, during and after the existence of everything else but she is most commonly associated with Parvati as evidenced by the various episodes of the Devi Bhagwat Puran. In fact how she gets the title of Durga is also mentioned in one of the episodes.
Devi Bhagwat Book 5 Chapter 23 mentions:
1-7. Vyâsa said :-- O King! When the tormented Devas praised thus, the Devi created from Her body another supremely beautiful form. This created form, the Ambikâ Devî, became known in all the worlds as Kaus’ikî, as She came out of the physical sheath of the Devî Parvatî. When Kaus’ikî was created out of the body of Parvatî, the Parvatî’s body became transformed and turned out into a black colour and became known as KâIikâ. Her terrible black appearance, when beheld, increases the terror even of the Daityas. O King! This Devî is now become known in this world as Kâlarâtri, the night of destruction, at the end of the world, identified with Durgâ, the Fulfiller of all the desires.
Goddess is named Durga:
In Devi Bhagwat Book 7 Chapter 28 Goddess Parvati transforms into Shatakshi (one with a thousand eyes) & Shakambhari who then faces 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.
It is after she destroys Durgam that she gets the epithet of Durga.
Furthermore, in the same episode, there is also the appearance of many other goddesses from Shakambhari Devi which shows that she is no different from the Adi Shakti:
At this moment, came out of the body of the Devi, the principal Shaktis (forces incarnate) named Kali, Tarini, Tripura-Sundari, Bhuvaneshwari, Bhairavi, Chinnamasta, Dhumavati, Bagalamukhi, Matangi and Kamalatmika. The Navadurgas Shailaputri, Brahmacharini, Chandraghanta, Kushmanda, Skandamata, Katyayani, Kalratri, Mahagauri, Siddhidatri and Matrikas Brahmani, Vaishnavi, Maheshwari, Kaumari, Indrani, Varahi, Narasimhi, Shivadooti, Chamundai also came out of the Goddess.
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.”
Also, Lakshmi and Saraswati find representation among the Dash Mahavidyas - Tara is known as Neel Saraswati and Goddess Kamala is the Tantrik version of Lakshmi
So going by all these concepts, it would appear that your second option is the most accurate one.