Now speaking as someone with a science education.

• In science, the closest thing to common-sense "facts" are proofs within an axiomatic system, of which 2+2 = 4 would be an example. Even there, you can run into problems, for example conflict between axioms which may or may not be resolved by modifying the axioms.
  
• In science, things get more vague if you include reality, that is, observations. What you do is creating hypotheses to create hypotheses describing past observations and predicting the outcome of future observations, and then decide which hypotheses are useful and which among the useful is best based on those future observations. Such a hypothesis is an axiomatic system itself, but you don't just judge it for internal consistency but also its relation to reality and to rival hypotheses. The adoption of a hypothesis that survived some tests may be considered akin to "fact", but one with inherent uncertainty. Due to that uncertainty, it could also be considered to be akin to "belief" (except a superseded scientific theory can still be useful: see Newton vs. Einstein), though the intuition of a researcher that this or that hypothesis is worth to be pursued is closer to common notions of "belief".

This is a weaker distinction of "fact" and "belief" than in common sense, but I find it even more difficult to do the opposite and apply the above two to religion. Very little prediction and verification and little competition is involved in the establishment of religious belief. Meanwhile, while theological debates are pretty much constrained to dogma and/or scripture and thus an axiomatic system, religious dogma and especially scripture is very elaborate as axiomatic systems come, and interpretation has a lot of room: is a certain passage allegory or history? Is a particular group of evil people denounced for apostasy, rape or homosexuality? What to make of slavery in the Bible? And so on. The relationship to reality is usually in the form of behaviour prescriptions derived from the axiomatic system, rather than the feedback of observations.

Now what you seem to be thinking of is collisions between scientific "facts" and religious belief. Like creationists seeing the Flood where geologists see processes like erosion over hundreds of millions of years, most other Christians believing that their God played an active role in the emergence of both life and humans while science is looking into hypotheses of abiogenesis and sees man as just one of the apes, Muslim literalists believing that children originate from their father's seed only with the mother only modifying the foetus while science says that the mother's ovum and the father's sperm fuse (with the former bringing in more genetic info), Hindu fundies saying that all species exist forever while science says that they evolve and branch out and go extinct all the time.

_{*Lunatic*, n.
One whose delusions are out of fashion.}