Just because a million people know or have heard about your brand, it does not mean that each and everyone is a part of your community.

Your community consists of people who are connected to your company directly. These people will have a sense of belonging, being a member of their own accord. These people are the reason why businesses around the globe invest so heavily in communities — to maximise brand loyalty of their customers and gain more hardcore fans of the brand who they can estimate to be lifetime consumers.

In short, the brand reach is the number of people who know about your organisation.
Whereas a community consists of members who have a direct relationship with your brand — as a customer, user or even an employee.