[detaro]

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, ...