The difference between the Mirror API and the forthcoming GDK boils down to where the application being written will run.
The Mirror API specifies how a web-based application will communicate with Google's servers to send updates to a user's Glass and how it will receive notifications when the user takes an action (such as a share, or a location change) that is directed at the Glassware.
The GDK is intended for applications that will run on Glass itself and have more low-level access to the sensors and to the underlying Android environment that Glass is built on top of. Google has not released the GDK yet - that page is where it will be released, and provides some early "getting started" concepts for developers who are interested in building native apps that run on Glass.