Scientific beliefs are repeatable and testable. Simply, you are told not to mix household cleaning agents, but you do, and you pass out. After recovering, and you repeat the process, and you pass out again. The danger of mixing household cleaning agents is based on repeatable scientific experiments. When you believe such things you hold a scientific belief.
Note: In science, the present "fact" is for now the best explanation, until a repeatable experiment proves different. With superstitions, the beliefs hold forever and forever with no need to prove it.
re. Superstition and "Old Beliefs," a superstition is generally foolish and irrational, passed along without questioning the sense of it. The fear of black cats crossing one's path is a good example of a superstition.
On the other hand, old beliefs may be part of an old religion that has been superseded by a newer religion. In their old religions, Greeks and Romans worshiped many gods. Those "old beliefs" were replaced by Christianity.
In yet another sense, an "old belief" could be something that was commonly thought to be true, that has since been proved false. For example, the idea that the common cold is caused by getting wet feet is an old belief that people no longer believe, since science has shown that the common cold is caused by a virus.