Difference to what?
You're speaking in code.
Theism is not a religion. Atheism is not a religion. And Non-theism is not a religion.
Religion is no more than a set of concepts and ideas that you live by and what you think others should live by. So yes, each atheists do have religious beliefs. But it is highly unlikely that all, or even most, atheists practice the same religious belief!
The same can be said about theists and non-theists as well.
I don't think I need to explain how this would define your politics
The OP contained a common bit of confusion, and I congratulate you on spotting it. There is a difference between "God-talk" and faith traditions. I think the OP was speaking of God-talk, but many regard faith traditions and religions as identical. Granted, there is a huge overlap, but they are not. I think the discussion of environmentalism as a religion is also a good example of the confusion.
So let me propose the usual definitions.
1. A "philosophy" is an organized cognitive structure to make sense of the universe. It is very close to the idea of a "world-view" but there are slight differences. With this definition, all religions must be a philosophy, but not all philosophies must be religions. Examples of philosophies that need not be religions include philosophy of science, formal logic, ethics, and historical analysis.
2. A "religion" is a member of a subset of philosophies that involve God-talk as a major element. These usually care several "badges" or indicia, such as creation myths, the existence of supernatural beings and phenomena, and the belief that the believer's future can be changed by manipulating such supernatural beings through cajolery, sacrifice, and worship.
3. A "faith tradition" is a set of beliefs founded on some axioms whose "truth" can be supported but not proven by "evidence". Usually a faith tradition has some organized method of transmission. The functional purpose of a faith tradition is to provide a narrative of meaning to life and to serve as a guide to behavior. Generally, faith traditions include a religion, and/or a philosophy.
Now there are a substantial number of faith traditions that that are not religions because they do not involve God-talk. Examples would include most Buddhism, Taoism, and Confucianism, as well as the Ethical Movement. Eighteenth century Deism comes very close to this class and I would include many Enlightenment thinkers such as Jefferson and the Philosophical Radicals (Bentham, both Mills, Locke, Smith) in this group. In addition, on a functional level I believe many "Christians" behave very close this manner. They stay away from theology as much as possible, expending effort instead on Christian ethics (Sermon on the Mount). These are all faith traditions that at most are marginally religions. In this I would agree with religious purists and fundamentalists, but instead of the characterization having a negative connotation, I would say it was either neutral or positive. In my observation, Christians who burn witches are more likely to be obsessed with Leviticus or Revelations than the Sermon on the Mount.
To your comment that Theism and Atheism are not religions; you are obviously correct. First, both terms assume a common definition of God. We are probably almost all atheists with respect to Jupiter, Thor, and Isis, although I must confess an attraction to the existence of Bacchus. The terms have no meaning without an explicit object of the belief or non-belief. They are classes of belief systems. Many theists subscribe to a religion, but not necessarily all, and certainly not all the same religion.
Now my definition of religion is a bit narrower than yours. As you defined it, a religion is identical to a belief system, which, I have just argued is not true. All religions are belief systems, but not all belief systems are religions (i.e. those which eschew God-talk are not religions).
And finally, I think that most political ideologies are belief systems, ways of viewing the world, and that many become religions or adjuncts to religions. Himmler and the Nazi belief system come to mind as an extreme example, and the Christian Identity movements.
So I am in substantial agreement with you, and just trying to a bit of clarification. Live long and prosper.