There's Adobe Edge Code CC - I thought that these were pretty much off the same code base?

They are. Brackets was presented at a local js meetup a little more than a year ago; Edge code is one of the primary reasons why adobe is running this project.

So I don't understand, Brackets is their open source branch but Edge Code will be their officially supported release?

Brackets, the open source project, supplies the core of Edge Code which has added features that tie into Adobe services.

We want Brackets to be awesome and useful by itself, and to also provide the foundation for people who use the Creative Cloud.