What is the difference between a fireplace and a hearth?

A fireplace refers to an exterior firebox for burning wood. It has front opening doors, where we can put in logs of wood and set it on fire. A hearth, which comes from the Old English word “hearth,” is defined as: “the floor or projecting part of any place that was used originally for cooking” (OED), but now usually means either: “The sunken rectangular space at the four corners of a chimneypiece, often incorporating flues or ovens; The hollowed-out recess with stone edging into which such spaces open” (Merriam Webster). So essentially hearths are flat surfaces used for cooking, and fireplaces contain a firebox with front opening doors.