One's worship system consists of the focus of his attention, be it God, status, exaggerated scarcity (like money), himself, or something entirely imaginary like a view of one's past.
A worship system can be evaluated by how much time, energy, and worry one places in something on a daily basis.
Belief systems may simply be an imprecise descriptions of underlying worship systems.
Atheism is a lack of a worship system. Anti-theism is a hatred of theism and any sort of worship system it typically entails self-devotion, censorship of criticism of evolution, and opposition to prayer. Though most Anti-theist are also Atheist they both don't mean the same thing. None-theist are people who don't subscribe to any worship system and often distance themselves from the other two groups whom they regard as theisms in some cases.