Compared to diffuse reflection, specular shading is dependent on the viewer's perspective. An example of specular shading would be reflections in the mirror, which are different when viewed from different angles; an example of diffuse reflection would be sunlight reflecting on the lake's surface.

I'm confused about which is the Phong model and which is the cheaper approximation. Is this formula being applied pixelwise?

Here's an article that helped me understand the importance of h or the "halfway vector". (https://learnopengl.com/Advanced-Lighting/Advanced-Lighting). From what I read, I believe that this image here is the cheaper "Blinn-Phong" model as opposed to the original Phong model. The intensity is highest when the normal vector is bisecting the light source and view direction. As a result, efficiently computing the halfway vector between v and l and comparing its angular difference to the normal vector can provide a metric for intensity.

Here it explains how shiny surfaces produce highlights by reflecting light toward the camera when the half vector (h), which bisects the angle between the viewer direction (v) and light direction (l), is close to the surface normal (n). This proximity is quantified using the dot product, yielding the intensity of specular reflection based on the light's distance and the surface's shininess. The formula given includes a specular coefficient and the angle of incidence to the power of 'p', which controls the shininess, with larger values creating tighter, more concentrated highlights, simulating a glossier surface. This model is a cornerstone in computer graphics, used to add realism to rendered images by simulating the way light interacts with different materials.