I'm confused has to what the difference between light casters (point, spotlight, directional) and lighting models (phong, gourang, global illumination). From what I understand both emit light in a scene. When would I choice spotlight over phong lighting. Whats the defining differences between the two concepts (light casters and lighting models)?.

A light caster, or light source, is just an object that emits light. A lighting model is a mathematical description of how light interacts with a surface. They are two different things.

You choose a light source type depending on what you need and are trying to simulate. A spotlight simulates... a spotlight. I think that's pretty obvious.

You choose a lighting model based on what lighting effect you want to achieve... whether it's more or less realistic, more or less computationally intensive, etc.

So are phong, gourang, global illumination the only major lighting models available (Or used by triple AAA titles). I've tried googling and these are the only ones that a the most common. If you could compile a list or link me to the right destination that would be appreciated.

A good starting point would be this book http://www.realtimerendering.com it covers a lot of different topics.
Lighting models like phong and gourad are local illumination models. Which means all objects are shaded independently.
Modern engines are using physically based lighting models which are a lot more complex than phong. If you are interested in that I can recommend this http://www.frostbite.com/2014/11/moving-frostbite-to-pbr/. Be aware that you should be comfortable with phong before starting with PBR.
Global illumination works quite different. For example movies use ray tracing to calculate images. Instead of lighting individual objects like in local illumination, you calculate how light rays move through the whole scene.