A RAT (short for Remote Access Trojan) is malware that gives a rogue operator access to a system. You can think of a RAT as a kind of Teamviewer, but used for malicious purposes. The term backdoor is also used for this kind of malware, though this term is also used for remote access built into a system, either by mistake or in secret.

A downloader is malware that downloads other malware. A lot of malware infections take multiple phases, where each malware downloads the next malware until the final one does the real task. For the malware operators, this has the advantage of the malware more likely staying hidden, while also allowing to have different kinds of malware downloaded on different systems.

Finally, a collection of systems infected with the same malware and operated by a single operator is called a botnet. In that case, individual systems in the botnet are referred to as bots.