In most (if not all) Debian based Linux distributions, the default browser is Iceweasel. What is Iceweasel? A rebranded Firefox. Why does it have to exist? Read this. (I honestly don’t know how accurate that is, but I’m assuming it’s at least mostly true.)
Here’s a screenshot from CrunchBang Linux, which is Debian based and therefore comes bundled with Iceweasel:
The Big Question however is if you’re running Iceweasel, do you even need to bother using Firefox at all since it’s more or less the same thing?
Answer: A conditional no.
The only time you would ever need Firefox instead of Iceweasel is if the newer version of Fx has some feature in it that Iceweasel doesn’t (yet). But the chance of that happening is very slim.
So anyway, no, you don’t need Firefox if you already have Iceweasel. And similarly, you don’t need Thunderbird when you already have Icedove.