Who is Chamunda and Chandika? Are they separate entities? I recently read Durga prayers, so I guess Chandika is incarnation of durgamata. and Ravana asked boon from arvatimata to protect lanka as chamunda as per serial of sankat mochan mahabali hanuman. No guarantee for veracity. Are they different?
Chandika is Ambika ,Devi or the supreme mother goddess who killed asuras like Shumbha ,Nisumbha,Raktabeeja and Mahishasura.
Chamunda is goddess Kali.She obtained this name after she killed the two demons named Chanda and Munda.Chandika herself gave Kali that name.
The Markendaya Purana(Chapter 87) has all the details.
After the mighty demon Dhumralochana was slain demons Chanda and Munda were sent to the battlefield to fight with Devi Chandika.
Sumbha, king of the Daityas, with agitated lips thus commanded the great Asuras Chanda and Munda. 'O Chanda and Munda proceed attended by a large body of forces, go and swiftly bring her here. Either lay hold on her hair, or hand, if you suspect the issue of the battle, with the various arms and the giants. Kill the wicked lion quickly, seize Amvika, bind and bring her to me.' Thus far is related in the sixth Chapter, mentioning the death of Dhumralochana, general of Sumbha and Nisumbha......The demons beheld her and highly exerted themselves to accomplish their designs, and the holder of the sword, and bow drew near to her. Amvika then became terribly angry at her enemies; rage changed her face into a hideous black. Her contracting brows overshadowed her forehead, the terrific faced Kali slung her Paca. She wore a wonderful Khutwanga, adorned by a string of human skulls, she wore a tiger's hide........The magnanimous goddess devoured or crushed all the forces of the valiant Asuras. She killed some with the sword, and struck some with the Khutwanga weapon; the giants died with the pressure of her teeth. In a moment all the forces of the Asuras fell; Chanda beheld it and ran to the frightful Kali. The mighty Asura, with a shower of numerous and tremendous arrows, and thousands of Chakras speedily enveloped the dreadful eyed goddess. Abundance of the discuses she swallowed, her face became as the orbit of the sun enveloped by the clouds. Then Kali, angrily shouted: her voice was horrible, her mouth became distended and frightful, and she gnashed her tremendous teeth. The goddess made her lion to rise, ran at Chanda, and laying hold on him by his hair, she cut off his head with her sword. After this Munda seeing the fall of Chanda, marched against her, she made him to fall on the earth and instantaneously killed him with her sword. The surviving forces perceived the fall of Chanda, and the valiant Munda, and through fear retreated in all directions. Kali took the heads of Chanda, likewise of Munda, and shoutingly exclaimed to Chandika. I have killed the great beasts Chanda and Munda, you will slay Sumbha and Nisumbha, in the sacrifice of battle. The Rishi said, she(Chandika) gently replied to the prosperous Kali, "as thou hast brought the heads of the great demons Chanda and Munda, you shall be renowned in the world by the name of Chamunda." Thus far is related in the seventh Chapter, comprising the death of Chanda and Munda.
So,Chandika is Ambika or Durga or the supreme Goddess where as Kali is a fierce form of Ambika .And Chamunda is one name of Kali.So,needless to say,Chandika and Chamunda are not the same deity.
To further illustrate that Chandika is different from Chamunda i quote the following passage from Chapter 88.
Chandika looked at the discomfited Suras, and speedily said, to Kali, "O Chamunda open your mouth widely. Great Asuras are produced by the drops of the blood of Rackta-Bija, you must instantaneously lick up the blood before it falls to the ground.......Chandika licked it up; Chamunda drank his blood. Devi by her trident, arrows, sword, and fists killed Rackta-Bija, and drank his blood....(Markandeya Purana Chapter 88)