Let me clear this up.

IRC - The chatting protocol and method.

mIRC - A program that allows you to access this chatting method.

QuakeNet - One of many servers that can be connected to that uses the IRC protocol. mIRC is one of several clients that can be used to connect to it. Any client that supports the IRC protocol is capable of connecting, but mIRC is most popular.

#jj2 - The chat "channel" on QuakeNet.

~ Traft