Debian – How to install Aurora (Firefox) on Debian

It's the same thing. See wikipedia. Basically, you are not allowed to re-compile the source code and still call it Firefox for trademark reasons.

You can use /etc/apt/preferences to specify which versions you want on a per-package basis.

To have the latest iceweasel version, use (at your own risk) the following configuration files:

/etc/apt/preferences

Package: iceweasel
Pin: release a=experimental
Pin-Priority: 1000

Package: *
Pin: release a=testing
Pin-Priority: 500

Package: *
Pin: release a=unstable
Pin-Priority: 400

Package: *
Pin: release a=experimental
Pin-Priority: 300

/etc/apt/source.list

deb http://http.debian.net/debian testing         main contrib non-free
deb http://security.debian.org/   testing/updates main
deb http://http.debian.net/debian unstable        main contrib non-free
deb http://http.debian.net/debian experimental    main contrib

But beware the the apt_preferences(5) manpage warns

Packages included in a specific release aren't tested in (and therefore don't always work as expected in) older or newer releases, or together with other packages from different releases. You have been warned.