Here is my understanding of the subject
Theism
Theism is broadly defined as the belief in the existence of a Supreme Being or deities. Theism
Non theism
Nontheism has generally been used to describe apathy or silence towards the subject of God and differs from an antithetical, explicit atheism. Nontheism does not necessarily describe atheism or disbelief in God Nontheism
Atheism
Atheism is, in the broadest sense, an absence of belief in the existence of deities. Atheism
Reason for asking
I have encountered a great deal of confusion surrounding this subject.
It appears non-theism gets confused with Atheism.
Many Atheists appear to use the term non-theism to describe themselves.
Many theists, label non theists as atheists, and atheists and non-theists.
However my current understanding is that silence and apathy towards the subject, is not the same thing as declaring belief, or, disbelief?