Update
As of March 10, 2016, Iceweasel has been discontinued, as reported here and elsewhere, and confirmed by the Debian Mozilla wizard. I'll leave this answer for historical information, only.
Standard Firefox and Firefox ESR 45 have been uploaded to Debian Unstable (as new source packages), and will follow the established testing route. Both will be available in all Debian distributions (Unstable, Testing, Stable, and Old Stable), via appropriate entries in the sources list.
People using Iceweasel from Debian unstable will be upgraded to Firefox ESR (a surprise, since the default Iceweasel version in both Unstable and Testing was recently based on standard Firefox, see edited original answer). Debian Stable will receive Firefox ESR after Iceweasel/Firefox ESR38 is deprecated, in about 3 months.
Original Answer
After posting my "recommended" answer, I realized that I didn't directly answer the question in case somebody else wanted that information. I'll do that here, starting with some context.
Edit: It appears that Debian revised its versioning of Iceweasel. I've incorporated changes below. The information reflects versions and code sources in February 2016.
Iceweasel Versions
Iceweasel is essentially a rebranded Firefox, although there are a few differences. It originated from a disagreement between Mozilla and Debian over use of the Firefox trademarks after Debian modifies and recompiles the Firefox source code. Other than the branding, the main difference is that Iceweasel does not include some of the third-party additions that Mozilla bundles with Firefox, such as Pocket.
There are now three versions of Iceweasel:
Iceweasel Beta is based on the beta release of Firefox. It is not intended for normal use by typical users. It is basically just to get a jump on testing. It lives in Debian Experimental (see below).
Aurora appears to no longer exist. It was based on the latest release of Firefox as a way to make that available when Iceweasel was based on Firefox ESR. It lived in Debian Experimental. However, Iceweasel based on the current standard Firefox is now available in the regular repositories.
Iceweasel (referred to as "Release" in the selection wizard), is now based on standard Firefox and is available in the Unstable and Testing repositories.
It isn't yet clear whether it's released in both simultaneously or graduates from Unstable to Testing after a brief evaluation period. It reflects the current Firefox version but it isn't yet clear how much delay there is. At the time of this edit, we are a month into Firefox 44 and Iceweasel 44 is the version in both repositories.
Iceweasel ESR is based on Firefox ESR (Extended Support Release), a version that is on a much longer major release interval than standard Firefox (currently about once per year vs. 6-8 weeks for standard Firefox). It is the Debian Stable version of Iceweasel.
As of February 2016, Iceweasel ESR is based on Firefox ESR version 38, which was the last ESR release. Version 38 was originally released in May 2015 but has been patched and received security updates as recently as January 2016. The next version of Iceweasel ESR will be version 45, associated with the next Firefox ESR, which is scheduled for release in March 2016.
Debian Distributions
Debian has five categories of "distributions" (in quotes because one isn't actually released), including three active releases.
Experimental contains packages and tools that are still being developed, and are still in the alpha testing stage. Experimental isn't a complete distribution. It is a staging/collaboration/experimental area for development, when it is known that a package has problems or may have problems.
Unstable is where active development of Debian occurs. This is where third-party software starts (or graduates from Experimental), when it hasn't been tested but doesn't carry an expectation of problems.
Testing contains packages that haven't been accepted into a "stable" release yet, but are in the queue for that. Users who want newer versions of software use this distribution, essentially contributing to the beta testing. Some other Debian family Linux distributions that want to offer newer versions of software (like Ubuntu and LMDE), are based on Debian Testing.
Stable is the latest officially released distribution of Debian.
Old Stable is the previous stable release
Availability of Iceweasel Versions in Debian Distributions
Although the different Iceweasel versions are associated with specific Debian distributions, they can be accessed in other Debian distributions in most cases. More-stable versions are usually available in the main repository for each Debian distribution. Less-stable versions of Iceweasel are usually available through backport repositories. "More-stable" and "less-stable" refer to the code source, it isn't meant to imply anything about quality.
The exceptions: Nobody uses Debian Unstable for the oldest, most stable software, so Iceweasel ESR is not available there. Similarly, nobody sticks with the Old Stable version of Debian if they want "experimental" software, so Iceweasel Beta is not available there.
As noted in the question, Debian has a wizard here for obtaining the Iceweasel version you want for the Debian distribution you're running (which, unfortunately, lacks any explanation of what the options mean; hence, this question and this answer). Note that the wizard does not appear to reflect the changes in versioning, so its results may be unpredictable.