If you previously establish that the vulnerability was introduced by a third party, then "backdoor" might be an OK term afterward - after the context has been introuced.
In an example without context (like, a headline), "backdoor" strongly implies that it was built by the vendor. I have to disagree with you and concur with the other commenters saying this was a very misleading choice of words by Kaspersky. They should have just said "malware".
I agree. My first reaction when I read the headline was, I thought Apple had put it there, which I found disturbing seeing as how Apple has publicly spoken out against backdoors. I think a better title would be something like "Sophisticated OS X Backdooring Malware Discovered". That would make it clear that the backdoor is not present in the binaries shipped by Apple.
I make the same association. A door is part of a building, and is put there during construction (initial release) or in owner-planned renovations (software updates).
I've never heard of someone breaking into a building by cutting a hole into a wall to install their own entry door that they have a key to, but that's the scenario this "OS X backdoor" is describing.
Rootkit is more commonly used for something that actively messes with the system to avoid detection for itself and potentially other malware, often by intercepting system calls and removing evidence from the responses.
Malware that just runs some code to provide a backdoor isn't necessarily a rootkit. E.g. if I install a VNC server on your system and turn off the tray icon, it is a backdoor. I could use a rootkit in combination to also hide it's files on disk, remove it from process listings, hide it's open sockets, ...
A rootkit is a different beast. A backdoor is simply a (covert) way to gain remote access to a system. A rootkit involves being able to elevate user permissions such that you have full control over the computer. Rootkits also typically use such permissions to hide themselves from normal user accounts.
I guess in a way you could see them as related, in that they both are access tools. A backdoor gets you remote access to the system in the first place. A rootkit gets you elevated access after you are in the system.
A rootkit is the thing you install once you have root - not a way to get root initially. It usually gives the attacker a means to access the machine in the future, even if the vulnerability she used is fixed in the future.
Rootkits are designed to hide themselves. They are essentially attacker installed backdooors.
A backdoor is basically a rootkit that is part of the original software as written by the original developer. The words have different connotations (rootkit is extremely negative, backdoors slightly less).
"A rootkit is a collection of computer software, typically malicious, designed to enable access to a computer or areas of its software that would not otherwise be allowed (for example, to an unauthorized user) while at the same time masking its existence or the existence of other software."
"A backdoor is a method, often secret, of bypassing normal authentication in a product, computer system, cryptosystem or algorithm etc. Backdoors are often used for securing unauthorized remote access to a computer, or obtaining access to plaintext in cryptographic systems.
A backdoor may take the form of a hidden part of a program,[1] a separate program (e.g. Back Orifice may subvert the system through a rootkit), or may be a hardware feature.[2] Although normally surreptitiously installed, in some cases backdoors are deliberate and widely known. These kinds of backdoors might have "legitimate" uses such as providing the manufacturer with a way to restore user passwords."
No, that is really wrong. Rootkits aren't for privilege escalation, see the paragraph immediately following your quote:
"... an attacker can install it once they've obtained root or Administrator access."
Calling BO a backdoor is a major corruption of the word, as you loose the only word for describing intentionally weakened security - so that you may describe a thing which already has several more explicitly defining names: malware, trojan, dropper, etc.
The installation of the rootkit is different from its purpose. A rootkit may require a root permission to install, perhaps piggybacking on another legitimate install such as in the famous Sony BMG rootkit. Or it may use an exploit to gain root access and install.
However, once installed, the purpose is the same: To provide the attacker with root permissions. It will also typically use its access to root permissions to hide itself from detection.
There are too many "No, that's wrong"'s here for a bunch of people that aren't getting this quite correct. You do not need root access to install a rootkit, you simply need to exploit a security flaw that allows you to install, run, and avoid detection. This is easiest done by modifying the host to disable it's ability to even find you on the device. This is much more difficult on modern systems, so for most modern systems, they're installed as trojans using the privilege escalation of another application or install.
The connotation difference is the difference between getting hit with a 10mm and a 9mm. Negligible, as it's leaving a hole that you really don't want there.
No, it refers to different things. Back-door is a technique or practice and a rootkit is a type of malware. Rootkits often (but not always) install backdoors.
In an example without context (like, a headline), "backdoor" strongly implies that it was built by the vendor. I have to disagree with you and concur with the other commenters saying this was a very misleading choice of words by Kaspersky. They should have just said "malware".