In Syria there is a difference between Baba Ghannouj and Mtabbal Al-Bathenjan, maybe in some countries they use both names for one dish, but here is the difference:
Mtabbal Al-Bathenjan (Mutabbal): prepared from grilled eggplant, yogurt, tahini and crushed garlic.
Baba Ghannouj (Baba Ghanoush): prepared from grilled eggplant, chopped parsley, chopped mint, chopped green pepper, chopped onion, crushed garlic, chopped walnuts, pomegranate arils, chopped tomatoes, pomegranate molasses, lemon juice, olive oil, and garnished with chopped walnuts, pomegranate arils, and olive oil.
Let’s make Baba Ghannouj: