When do Muslim women wear the Burqa, Hiyab, Niqab or Chador? Are these pieces of headwear representative of different Islamic sects, or are they worn by the same women in different circumstances?

For example, is one style worn around the house, one for when she is out in public, and one for the mosque? Is one more formal than the other? Or are these different pieces of headwear worn by different groups exclusively as sect identifiers such as a Sunni female wears only the burqa or a Shiite female wears only the Hiyab?