I have no idea how people have been combineing RAT's and botnets to mean the same thing...
RAT = Remote Access/Administrative Tool/Trojan
It's the peice of software, ususally a virus, that goes on a target's computer.
A botnet is a collection of comprimised computers, usually created by spreading a RAT.
If you need a good rat that's not already detected to hell, I've been told that GO (google's new programing language) does a lot of threading+optimization automaticly, so it can handle tons of clients.
Also, a botnet is for more than just DDoS, dependent on the RAT on the client side, they can be used to get a site to the top of google, or other search engine, to mine bitcoins, or any other task that needs the use of lots of processing power, bandwidth, or unique IP's.