A Brasserie is usually a large, bustling place with a traditional menu, where the food is good, but not necessarily served in the way of Michelin starred restaurants. In general, brasseries are open all day long, all days of the week.
A Bistro is a smaller and more personal restaurant with the intentions of creating original imaginative dishes. They aren't necessarily open all day or all days of the week.
Restaurant is a generic term for places that serve food, including Brasseries and Bistros.