Science differs from religion in that WE can change our minds. Religion, because its primary reference book is ESSENTIALLY unchanged in the last couple of millennia, cannot. Despite the Book of Mormon, we have no reason to believe that ANYONE has had a credible religious visitation since the Council of Nicea. (Joan of Arc was burned at the stake for making such a claim; Bernadette was ridiculed for it.)
Science can say, "Oh, darn, looks like the phlogiston theory is wrong." (No, I didn't make up that word.) Religion CANNOT step away from its claims such as the Christian/Judaic "Exodus" from Egypt. Israeli archaeologists, who had a vested interest in CONFIRMING that the Jews are, indeed, the chosen people, had to finally conclude that there is NO HISTORICAL EVIDENCE of Hebrew slaves ever being in Egypt in the first place.
Science can say, "We have learned more about medicine; there are these little things called GERMS that cause disease." Religion CANNOT add to its knowledge because (taking Christianity as an example) the holy books claim that you should not take away from or add to the books.
Science can say, "Oh, darn, looks like physics isn't as deterministic as we first thought; it is more probabilistic." Religion CANNOT change its story on the Great Flood, even though that story simply CANNOT explain how after a flood wiped out all creatures everywhere other than in the ark, we found a plethora of species in North America, South America, and Australia - not to mention many of the larger oceanic islands - even though there were NO land bridges for mammalian migration. I guess someone taught the kangaroos how to do a long-distance backstroke?
Science is not a religion; it says nothing about spiritual matters (other than saying that there does not appear to be anything to the idea of a soul in the religious use of that word.) Technically, science doesn't rely on theories. It relies on facts and uses theories as a possible way to explain those facts in a self-consistent way (and I DID say "possible", not "definite").
Here's the biggest difference between science and religion. Joan of Arc was burned at the stake for recantation and later reassertion of her non-orthodox views. Galileo was censured and placed under house arrest for daring to dispute religious beliefs. Opposing religions have gone to WAR over minor differences in doctrine.
What happens when you recant in science? You not only get a publication out of it, but you get ANOTHER publication when you make a correction. What happens when you and another scientist disagree? You both go back to the lab and do more research and come up with more publications. And if it is interesting enough, you get a grant for it.
At base, the difference is flexibility vs. intransigence, and let's not get into questions about proof.
