This is a good question. Belief systems can be the same as religious beliefs, but they do not necessary have to.
If you look at religions, they do have a belief system. For example, Christianity has a creation story, an explanation for why the things are the way they are, a theory of salvation, and moral imperatives. The same can be said for all the major religions of the world. So there is a belief system, even if there is great flexibility within all religions.
Now some belief systems, like communism, have a worldview and system of beliefs, but there is no idea of the divine. Therefore, it is very different than religion. In fact, something like communism is the opposite of religion; communists are atheists.
In summary, all religions have a belief system, but not all belief systems are religious.