What is the difference between Iceweasel and Firefox?

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.

Ice isn't fire, and weasels aren't foxes, but IceWeasels and Firefoxen are the same thing. Apparently it's IceCat now. Also be on the lookout for Icedove, Iceape, and Iceowl.

Debian refused to use Firefox's logo because it is not free (as in speech, not as in beer), and in turn Mozilla said that they can't call it Firefox if they're going to use their own (non-Mozilla-approved) logo, so they called it IceWeasel.

http://en.wikipedia.org/wiki/Mozilla_Corporation_software_rebranded_by_the_Debian_project

Update 2016, and onward.

What is the difference between Iceweasel and Firefox?

• The short of it In 2016, Iceweasel went away, and now for all of Debian's purposes the product is called Firefox, and the package is called firefox-esr. The package is described as "a powerful, extensible web browser with support for modern web application technologies."
• Useless Historic Backstory Ice Weasel was an old name that refers to more of a fork of Firefox because Mozilla wanted to protect their trademarks. Firefox automatically updates from Mozilla; Ice Weasel updates through the repository. Mozilla at one point didn't like you calling things they viewed as being out of date, and not maintained by them as "Firefox". And Debian was applying patches that Mozilla viewed as being not strictly Firefox. Debian patches a lot of software to make them play well with other software they package, and all their software goes out through their own distribution channel. This is rather routine. In 2016, Mozilla relented and this changed their stance stating "Mozilla recognizes that patches applied to Iceweasel/Firefox don’t impact the quality of the product,". Mozilla had come to trust Debian, and to this day the Debian distribution is patched without regard to Mozilla's trademark concerns or approval, and distributed through Debian's official channels. It is disclaimed as being "modified from upstream by removing a set of sourceless binary, non-free, and VCS-related files."