Start with the construction, not the outside height
Bolsters, fluffy covers, and lofted fiber can make a bed appear thick without telling you how much supportive foam is underneath the sleeping surface. Look for the actual layer description and total usable support beneath the dog.
Material names are useful clues, but they are not a complete quality rating. Two beds described as memory foam can feel very different depending on layer thickness, firmness, underlying support, and the dog's size.