In the Durga Chalisa, it says that:
धरा रूप नरसिंह को अम्बा
प्रकट भई फाडकर खम्बा
रक्षा करि प्रह्लाद बचायो
हिरण्याक्ष को स्वर्ग पठायो
You Assumed the Form of Lord Narasimha,
And Appeared Breaking the Pillar You Saved Prahlada
And Sent Hiranyakashyapu to Heaven (as he was killed by You)
Now I am aware of the sentiment that all deities, are in essence the same. I have also seen specific references in other scriptures, such as the one below given in the [Shivakamasundari Sahasranama Stotra]:
ekaiva śaktiḥ parameśvarasya
bhinnā caturdhā viniyogakāle
bhoge bhavānī puruṣeṣu viṣṇuḥ
kopeṣu kālī samareṣu durgā
Which equates the form of goddess Bhavani with blessing devotees with all pleasures / desires, Vishnu as the masculine form of Devi, Kali as the manifestation of anger, and Durga as the manifestation on the battle field.
Are there are any specific sources that equate Devi Durga and Narasimha in any puranas?