Question: My class notes have made it clear that these two are not the same. I understand that the Phong Illumination Model is ambiant+diffuse+specular, but where does Phong Shading come into play when it comes to lighting? What about BRDFs?

Answer: 
Phong Shading is a method used to calculate the shading on an object.
To calculate the shading of a point on an object, the *normals of the vertices* are interpolated.
In comparison, flat shading only uses the normal of the polygon. Phong shading will result in smoother, more curved edges while at the same time not requiring a lot of polygons.

Also see [this article](https://opengl-notes.readthedocs.io/en/latest/topics/lighting/shading.html) and especially the picture.
The shading model computes the reflected light at a single point, by accounting for the ray and surface directions and reflectance characteristics.

The interpolation method is made to compute the reflected light between points where the normal is known. You distinguish

* Gouraud shading: you evaluate the light color using the reflectance model at the known points, and interpolate on the color;
* Phong shading: you interpolate the normals and apply the reflectance model at every interpolated point.

Phong is more costly but more realistic.