Further clarification: Yes, people do die from smoke inhalation. In fact the National Fire Protection Association (NFPA) which also writes many of the regulations fire departments follow, lists Smoke Inhalation as the #1 cause of death in a fire.

However, the poisonous gas that Shawn discusses is a component piece of that smoke. The smoke and particles can impair respiration and the fumes and other gases further complicate breathing. Ultimately, the person asphyxiates.