I think this is off-topic, but here is what you are looking for.
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. - you might use it for keeping your access to a compromised system after exiting or logging out from that system by having a port set for giving you shell and access or whatsoever else again. Meanwhile once an attacker gains root privilege, it becomes a cakewalk|backdoor for him to exploit (used as verb) your system. BTW, there is a slight difference between RootKit and BackDoor.
In computing, an exploit is an attack on a computer system, especially one that takes advantage of a particular vulnerability that the system offers to intruders. Used as a verb, the term refers to the act of successfully making such an attack.
It is easy to juxtapose terms which are somehow related to one another. It is best to learn the precise meaning of certain words. Although this is more work than not using those words correctly, doing so allows us to communicate to others more clearly.
RootKit: Software that hides itself on a system so it is not easy to detect. Often used as a way to maintain long term control or access to a system that the system user is unaware of. A rootkit may use exploits to either gain initial access or complete control of the system.
Exploit: An unpatched vulnerability in a system (in hardware, OS, or application code) that can be used by an attacker to gain access to, control of, or escalate privileges on that system.