In the past, each model's characteristics resembled more closely a certain type of material, for example Phong could be used for plastics, Ward for cloth and metals, and Blinn for other common surfaces. The GGX model has a bright center and an even longer falloff (at default settings).
The Ward model has an even broader center and falloff. The Blinn model has broader highlight center with a tight falloff.
For example, the specular highlights with the Phong model have a very narrow and bright center with no falloff, but it doesn't work well with anisotropic reflections. Historically, the Phong, Blinn, Ward and GGX are successive reflectance models developed over the years in computer graphics where each model aimed to improve on the limitations of the previous ones.
