Running shoe shank
Purpose is to stiffens the shoe under the arch, which makes the middle portion of the shoe firmer (minimalist shoes doesn’t have it). Some of them wraps the shank up to the medial post part of the shoe to add more stability and thus allowing it to function more like a medial post.
Running shoe outsole
The main sole of the shoes that makes contact with the ground itself. Usually made up from durable carbon rubber, most of them has the same material as car tires, although more flexible and has a great tread for traction.
Different brands uses different kind of outsole, mainly for performance. Brooks uses a hard-wearing rubber calling it High Performance Rubber, and a softer rubber in the forefoot to aid cushioning.