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

There is no difference it is basically just a different name due to trademark issues - see the origins of the dispute.

However Firefox is provided by Mozilla whereas Iceweasel is provided by Debian.

While this question has been asked long back, things might have changed since then.

Is there any advantage of using Iceweasel and Firefox?

Is there any difference to the two programs?

What are the advantages and disadvantages to each program?

• Firefox is provided by Mozilla. Iceweasel is provided by the Linux distribution that offers it (debian*). If you have a distribution that has Iceweasel, then Firefox may not be present in its repos and installing Firefox on such distro needed to be done manually by downloading binary from Mozilla. In such a case, Updates for Iceweasel are provided automatically by distro whereas you need to update Firefox manually. Considering Security Updates for browser really important, this matters. Iceweasel is the winner.


• The current Iceweasel is based on Firefox Extended Support Release. Meaning that Feature Updates aren't available until they are well tested. Only Security Updates are deployed. Even before when there is no Firefox Esr, feature updates of Firefox didn't make it to Iceweasel. Organisations that use Iceweasel are benefitted by this. And recently Firefox has got many unnecessary additions like Pocket and Hello. Iceweasel also removes all of these.


• Mozilla will not allow the changed Firefox code to be compiled and released under the same brand name. Its reasonable. Hence Iceweasel came out with a different logo. But basically its Firefox with more stability and unnecessary components removed.

Which one seems better?

Its a personal choice. If u need stability and not concerned about new features then Iceweasel is the choice. If not, U may use Firefox.

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 amount to more of a fork 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."
  

Reportedly, Iceweasel and other variants generally are behind in versions compared to Firefox. That's a red flag for me. I tried to use Iceweasel to log into my credit union. Finally, it loaded--it took several minutes, even, though. (I proved surprised when it actually succeeded.)

Possibly a better solution exists: Some time ago, someone wrote some scripts to induce (more accurately, to "deceive") problem sites into "believing" that Iceweasel actually is from XP! It required changing to an enabled user--"on the fly"--just for such special situations!

I'd like to use Iceweasel: It must be kept up to date, though--otherwise, I just can't trust it. I believe that it lacks integrity: Recently, I couldn't kill the browser and also couldn't log out cleanly, either: I had to reset. FF likely would have performed better.

(A similar situation exists with clamtk--the current version of clamtk must be downloaded separately, from sourceforge.net. That's easy enough: But, why?! That's another issue, of course....)

I'm thus going to mozilla.org in order to obtain Firefox. I'll keep Iceweasel on, though: After all, it's the distro's official browser. I desire for it to succeed better.

Really, though, petty squabbling over logos, branding, and idiot legal manueuvering is just slapping the faces of so many who benefit the community so greatly! Fiefdoms:They weaken a community greatly and tarnish its ideals. Unfortunately, these great "code-wizards" merely are human and actually prove to be from earth, after all!