No they are not , they are both APIs. The fact they run on top of drivers is nothing impressive if anything they make a tiny fraction of the APIs Unreal depends on because it’s so much more than a 3D Engine. Unreal runs on top of Vulkan and could also replace both Vulkan and GPU drivers. API dependence is nothing special and hardly makes something so different. There is no limitation on how low level Unreal can go.
Unity and Unreal engines are both built on top of APIs such as OpenGL and Direct3D