Emergence of Kali was mentioned in Chapter 7 of Durga Saptashati/Devi Mahatmya.
ततः कोपं चकारोच्चैरम्बिका तानरीन् प्रति। कोपेन चास्या वदनं
भ्रुकुटीकुटिलात्तस्या ललाटफलकाद्द्रुतम्। काली करालवदना
Thereupon Ambika became terribly angry with those foes, and in her
anger her countenance then became dark as ink. Out from the surface of
her forehead, fierce with frown, suddenly issued Kali of terrible
countenance, armed with a sword and noose.
After a bitter fight, Kali chops off the heads of Chanda and Munda and brings the same to Chandika.
Chandika names her chAmunda for this act.
यस्माच्चण्डं च मुण्डं च गृहीत्वा त्वमुपागता। चामुण्डेति ततो लोके
ख्याता देवि भविष्यसि॥ॐ॥२७॥
So chAmunda and kAli are one and the same. As kAli emerged from Chandika, there is no difference between kAli and Chandika, as the fierce form of Chandika is kAli.
That was why the dhyAna mantra of chandika is
'ऐं ह्रीं क्लीं चामुंडायै विच्चे'
As per the idols, chAmunda Devi also wears garland of heads of demons.