https://en.wikipedia.org/wiki/Rootkit
"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."
https://en.wikipedia.org/wiki/Backdoor_(computing)
"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."