The majority of clay pizza ovens are wood-fired. The fact that they are fuelled using wood means the question of heat distribution around the food being cooked is a major concern. Based on this, burning charcoal is placed inside the oven, around the food being cooked.
Does it mean there aren’t clay ovens heated from underneath? Well, majority of the clay ovens have a lower (underneath) compartment where additional fire can be lit. This is necessary if it is being used for long, and the initial fuel placed in the oven stands to run out, especially in commercial units.
Nevertheless, there are barrel ovens which are heated from underneath. However, different from the other mainstream clay oven, the pizza floor has to be a good heat contactor to allow for heat transfer to the cooking food. Normally, in the case of barrel ovens, a drum is used and inside decks are added to provide placement for the food being cooked.
Further information: Wood Fired Pizza Oven Building Plans, Types of wood fired pizza ovens, and Clay oven pizza