The belief that no God or deity exists out of the context of physicality, in the same way a traditional atheist does. The Atheistic Buddhist however does follow the ways of the Buddhist philosophy.
Religious person: Hey! What religion do you believe in?
Atheistic Buddhist: I am a follower of Atheistic Buddhism.
Religious Person: What's that
Atheistic Buddhist: I don't believe in any God or Gods, but I still follow the teachings of Buddhism.
Religious Person: Ah! Interesting!