A bunsen burner is basically generates a flame of quite high intensity which is supplied by gas. Once lit by a match the flame can be made to burn very powerfully so that it can be used to heat up liquids.
A heater in which gas is mixed with air (whose amount you can regulate) before being burned. That makes it warmer than without the mixing with air. The name comes from the German chemist, Robert Bunsen, who invented it about 150 years ago.