The biggest difference, however, is that you can test a scientific interpretation, repeat a study, etc. You can be proven wrong or validated as right.
As it turns out, not all the time. In fact, not even all that frequently. Popper criticized the idea of verification, Kuhn criticized the idea of falsification, and neither idea solves the demarcation (between science and non-science) problem. For a quick reference that won't require a number of books, try this.
You see, it really doesn’t make any sense...
It doesn't make sense to you based on what your ideas of legitimate knowledge are - and you're making some major generalizations about how religion operates. For some religions there is a monotheistic deity, and for some of those religions the word of that deity is immutable law. But even in those cases, there is significant debate over what exactly constitutes the "word of God" - I mean, it's why there's so many different sects and factions (and even those argue internally). Just like in science, there are different interpretations of our observed world, and some interpretations become more dominant than others - and not always because they best align with our observations of the physical world.