I think when you mean flatbread you are referring to a chappati also known as roti. There are actually many variations in Indian bread and differ according to the locations and cuisines in India.
Some of the other variations are:
Prantha which is a cooked with lots of ghee or butter on it. It can be made plain or with a stuffing like cauliflower or potato.
Puri, is deep fried. It is smaller in size and normally accompanied with chickpeas curry or potato curry.
Bhatura is made from raised flour and is also deep fried. This is soft and fluffy and served with chickpea curry.
Tandoori Naan is another bread made from raised flour but it is cooked in a tandoor, this is served at near enough all restaurants in India.