Taegeuk is a name of the poomse/forms/patterns used by many Taekwondo schools. I believe this is the most common especially in WTF Taekwondo. Somebody else may know more.
Chonj-Ji is the name of the first or basic pattern from the Chang-Hon Taekwondo system. You will find many Taekwondo schools follow different systems so hence different patterns.
McDojo or McDojang is the name given to any school ... not just Taekwondo ... where you sign up on a big long term contract and put up big bucks knowing you will eventually get a black belt because you paid for it.