In Debian, Iceweasel is Firefox once again, since March 10, 2016. There's an Iceweasel branding add-on which can be used to restore the Iceweasel branding.
There are some non-cosmetic differences between Mozilla's version and Debian's; you can see all the patches here. You'll find changes which disable "phone-home" features (Firefox health report), change the way plugins and extensions are handled to work better in the context of a distribution with packaged plugins and extensions... There are also a series of bug fixes backported from work-in-progress upstream versions.
These are the kinds of changes you could find in any package in Debian (the old branding changes weren't, of course, although quite a few Debian packages include minor branding changes — e.g. adding a "Debian" mention in version numbers in gcc and Wine). The Chromium package for example also disables various "phone-home" features; many packages include backported bug fixes, and changes to integrate the software into the distribution.