The commentary to Srimad-Bhagavatam, 11.2.48 discusses this:
". . .the Brahma-samhita (5.44) says:
sristhi-sthiti-pralaya-sadhana-shaktir eka chayeva yasya bhuvanani bibharti durga.Maya is like a shadow of the Supreme Personality of Godhead who serves Him in the creation, maintenance and annihilation of this world. Just as a shadow has no independent power of movement but follows the substance that casts the shadow, the illusory energy of the Lord has no independent power, but bewilders the living entities according to the Lord's desire. One of Krishna's opulences is that He is supremely detached; when a living entity wants to forget Him, Krishna immediately employs His illusory energy to facilitate the foolishness of the conditioned soul."
Srila Prabhupada also identifies Durga-devi as Maya in his purport to Srimad-Bhagavatam, 3.23.57:
"Actually, the illusory, material energy is cheating everyone. People do not know what they are doing when they worship the material energy in the form of goddess Kali or Durga for material boons. They ask, "Mother, give me great riches, give me a good wife, give me fame, give me victory." But such devotees of the goddess Maya, or Durga, do not know that they are being cheated by that goddess. Material achievement is actually no achievement because as soon as one is illusioned by the material gifts, he becomes more and more entangled, and there is no question of liberation."
However, the name "Durga" doesn't always refer to Krishna's illusory energy by which we're all bewildered in the material world. For example, the cowherd girls of Vrindavan, the gopis, prayed to Durga in order to get Krishna as their husband. The gopis are well known as Krishna's dearest devotees, and certainly aren't ignorantly seeking illusory happiness. In Srimad-Bhagavatam, 10.22.4, Purport, we see this commentary on Durga and Maya:
"According to various acharyas, the goddess Durga mentioned in this verse is not the illusory energy of Krishna called Maya but rather the internal potency of the Lord known as Yoga-maya. The distinction between the internal and external, or illusory, potency of the Lord is described in the Narada-pañcaratra, in the conversation between Sruti and Vidya:
'The Lord’s inferior potency, known as Durga, is dedicated to His loving service. Being the Lord’s potency, this inferior energy is nondifferent from Him. There is another, superior potency, whose form is on the same spiritual level as that of God Himself. Simply by scientifically understanding this supreme potency, one can immediately achieve the Supreme Soul of all souls, who is the Lord of all lords. There is no other process to achieve Him. That supreme potency of the Lord is known as Gokulesvari, the goddess of Gokula. Her nature is to be completely absorbed in love of God, and through Her one can easily obtain the primeval God, the Lord of all that be. This internal potency of the Lord has a covering potency, known as Maha-maya, who rules the material world. In fact she bewilders the entire universe, and thus everyone within the universe falsely identifies himself with the material body.'
From the above we can understand that the internal and external, or superior and inferior, potencies of the Supreme Lord are personified as Yoga-maya and Maha-maya, respectively. The name Durga is sometimes used to refer to the internal, superior potency, as stated in the Pañcaratra: “In all mantras used to worship Krishna, the presiding deity is known as Durga.” Thus in the transcendental sound vibrations glorifying and worshiping the Absolute Truth, Krishna, the presiding deity of the particular mantra or hymn is called Durga. The name Durga therefore refers also to that personality who functions as the internal potency of the Lord and who is thus on the platform of suddha-sattva, pure transcendental existence. This internal potency is understood to be Krishna’s sister, known also as Ekanamsa or Subhadra. This is the Durga who was worshiped by the gopis in Vrindavan. Several acaryas have pointed out that ordinary people are sometimes bewildered and think that the names Maha-maya and Durga refer exclusively to the external potency of the Lord."
"The Brahma-samhita says, chayeva yasya bhuvanani bibharti durga. Durga is not different from yogamaya. When one understands Durga properly, he is immediately liberated, for Durga is originally the spiritual potency, hladini-sakti, by whose mercy one can understand the Supreme Personality of Godhead very easily. Radha krsna-pranaya-vikrtir hladini-saktir asmad. The mahamaya-sakti, however, is a covering of yogamaya, and she is therefore called the covering potency. By this covering potency, the entire material world is bewildered (yaya sammohitau jagat). In conclusion, bewildering the conditioned souls and liberating the devotees are both functions belonging to yogamaya." (SB 10.1.69)
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Śrīla Viśvanātha Cakravartī Ṭhākura:
In order to charm the eternal devotees and bewilder the enemies like Kamsa, Krishna gave orders to Yogamaya and Mahamaya. Being ordered by the lord Yogamaya and her expansion as the external energy Mahamaya, which bewilders the world, will appear.The sruti-vidya of Narada Pancharatra states that Mahamaya is an expansion of Yogamaya, Yogamaya is the swarupa-shakti of lord Visnu. She is completely surrendered and unswerving in devotion to the lord. Her nature is Prema (love) and she rules over Gokula like a queen. One immediately attains the lord by her mercy. Her avaranika-shakti is Mahamaya, the controller of the material realm. By her influence all Jivas identify with their material bodies and become bewildered. Mahamaya is also called Durga.
There are two types of activities: those of Yogamaya and those of Mahamaya, Yogamaya came to the prison when Krishna was born, transferred the seventh child from Devakis womb and put Yasoda into deep sleep to exchange the two children. These are activities of Yogamaya, not Mahamaya. Mahamaya does not have the power to transfer her master Balarama to another womb. Yasoda's sleep is not the work of Mahamaya because the scriptures say that beyond the fourth state of consciousness is the fifth state of Prema. The dreaming of Krishna's eternal associates occurs in the state of Prema. Their sleep and dreaming are not caused by the modes of nature. Mahamaya can't exert any influence over the eternal associates of the lord.
The form of Devakis daugher that Kamsa tried to kill, was Mahamaya not Yogamaya, Yogamaya does not involve herself with such sinful people. Mahamaya slipped from Kamsas hands, rose up in the sky and then settled in many places with different names after saying "I will be born from the womb of Yasoda in Nandas house in the twenty eighth Yuga-cycle at the end of Vaivasvata Manvantra. As a resident of Vindya-mountain, I will kill your evil companions.
The bewilderment of the husbands and mother in law of the married Gopis joining the rasa-lila was an action of Yogamaya not Mahamaya, because the husbands were not atheistic or unfavourable towards the lord. If they were under the influence of Mahamaya, then one would certainly observe in them hostility towards Krishna. On the other hand demons like Duryodhhana and Salva never gave respect to the lord, even though they saw Krishnas Viswarupa and Garuda, Vishnu's carrier. They thought Krsna was one of the wicked Yadavas. This is the action of Mahamaya not Yogamaya, because their actions show hostility towards the lord. Yogamaya means which connects to Krishna.
The bewilderment of the demons is the action of Mahamaya and the bewilderment of the devotees is the action of Yogamaya. When Yasoda saw the universal form in Krishnas mouth and when Nanda Maharaj saw Krishna in Visnuloka, they were completely unaffected by it because of their intense vatsalya-bhava parental affection, even though they saw such majestic aspects of the lord. This is neither the action of Yogamaya nor Mahamaya. It is the nature of Prema (love) itself.
Prema (love) covers ones knowledge of the lords power and majesty aishwarya mayi gyan, and binds up Krishna in the hearts of his Prema-bhaktas more and more with the ropes of spiritual possessiveness, as affection for Krishna increases, Prema completely submerges the devotees in the great ocean of relishing Krishnas sweetness. To convey this unique quality of Prema the Tantra-shastra says, Krishna spread his vaisnavi-maya in the form of parental affection. Extreme affection for the son is the unique quality of Vatsalya-prema. In this verse Yogamaya is refereed to as Maya since it shares the quality of spreading illusion with Mahamaya.
