Blinn shading is a subtle variation on Phong shading. The most noticeable difference is that highlights appear rounder. In general, you don't need to use the Soften parameter (described in Blinn, Oren-Nayar-Blinn, and Phong Highlights) as often as you do with Phong shading.
Blinn shading tends to have soft, round highlights.
With Blinn shading, you can obtain highlights produced by light glancing off the surface at low angles. These highlights are lost when you increase the value of Soften using Phong shading.
The Blinn and Phong shaders have the same basic parameters.