I don't think dogmatism (closed-mindedness, or reluctance to accept new ideas) compares well to irrationality (process of not using clear thinking, without reason.)

Keeping it simple, take the process of walking under a ladder, and the idea that it's bad luck. It might not be quite as safe as going around. But holding to a superstitious viewpoint that bad things will happen to you later because of this act is irrational. The closed-mindedness is of the holder of the superstition, as scientific data can show out that no, walking under a ladder doesn't create bad luck for your life. The dogma of the one who is superstitious is irrational, not the person determining the fear.

As for the superstition and belief being the same? No, I don't see that either. Superstition encompasses a belief (irrational as it may be) but belief does not necessarily include superstition. Neither mutually exclusive nor encompassing.