Clear Moon: A common thread between both games is some kind of mysterious secret society known as Clear Moon. In Dead Detention, they created the zombie virus and tested it on a block of New York. In the cannon Chaos Girl ending, they kill both Ami and the main character, as well as house, and cover up the existence of, the Armageddon Children.
Armageddon Children: As shown in Chaos Girl, they are beings sent down by a divine being to bring destruction to Universe 08. They obtain special supernatural powers. Clear Moon tries to export one from Tokyo to New York to help clear out the remaining zombies. Obviously, things didn't go quite to plan and she managed to escape.
Zones: Each major city in the world has a Clear Moon base of operations. So far you know of 2; Zone Zero in Tokyo, Japan, and Zone Three in New York. Each zone also has some kind of a leader. The leader of Zone Zero is known as "Commander Dia."
The Moon King: Some kind of Clear Moon higher up(?)
The Crest: The Crest appears in Dead Detention, Chaos Girl and the universe 08 logo. It's also the logo of my upcoming visual novel Clear Moon. This'll make more sense soon.
Chronicle Bulletin: In Dead Detention, Max looks up news stories about the zombie virus, and comes across an article on some kind of paranormal news website called Chronicle Bulletin.
New Heart High: A high school in Tokyo that Ami enrolled into, in order to hide from Clear Moon.
If you pay attention to background details you might also notice some other phrases and keywords that'll mean a little more later on.
After the final bonus episode of Dead Detention is up, I'll be starting it's sequel series; Chronicle Bulletin. This episodic series is set 3 years after the events of dead detention, and acts as a direct prequel to my big upcoming visual novel Clear Moon. Sora from Dead Detention returns in this series as a main character, along with 2 other new characters; a dude called Atom and a girl called Nova. All three students go to the same high school from Chaos Girl; New Heart High.
I'm also planning to create a bridging one-off visual novel that'll be set between Chaos Girl and Chronicle Bulletin. It'll focus on an Armageddon Child who managed to slip through the cracks of the Black Friday protocol.