[JohnFitzgeraldKennedy]

Rats and botnets are in essence the same thing, they are just malware that gives the controller persistent remote access to the target machine. I guess the only real practical difference that I could point to is that, in my experience, so called "RATs" have a GUI and lots more bells and whistles for directly interacting with the target machine. Botnets are usually more limited in their core commands/features, intended to be more modular, and intended to scale, so they usually have less functionality to directly do things like RDP onto a machine for example and are moreso controlled by issuing commands or tasks for the bots to pick up, eventually, which are performed asynchronously.