Here is how I describe the difference:
Each one is designed for a different business persona OR job role.

SAS Enterprise Guide is a drag-n-drop interface into the power of the SAS programming language used for ad-hoc analysis and reporting.
NOTE: Does not need to be a statistician.

SAS Enterprise Miner is designed specifically to make a data modeler job easiser which is to help create, assess, and then implement predictive or descriptive models.
NOTE: Needs to at least understand statistics to be successful.

The two definitely can be used together to compliment each role. SAS Enterprise Guide can be used for preparing the data before mining as well as using the model after mining to produce/automate reports.