The field considered by religion ? Well, it depends on who you ask…It depends on the religion you consider, too, as some religions simply are a philosophy of life.
To answer your question, maybe could it be interesting to start with the dogma of a considered religion. The dogma is a kind of thing which CANNOT be negated. Otherwise some pillars of the religion would fall apart.
One Christian dogma is the clearcut difference of nature between the body/flesh and the spirit. To support this, they ‘’invented’’ a story. Which is an approximation. But it is written down. Science can link cells & thoughts… (exit the Free Will …)
There are some instances, where the religious “story” is reconsidered (Galileo/ Copernic): The first approximation has therefore been “adjusted” in some way.
Within the fields of “spirit” and of “astronomy”, science & religion changed their approximations over time. Initially, “science” was what religion said. Only progressively did true Science took its independance.
Sometimes, Science & Religion seems to be doing the same job. For example archeology. The case of Biblical Archeology is interesting. Biblical and Scientifical archeologists work side by side, using the same professional techniques, on the same archeological sites.
The difference is in the methodology of analysis of the archeological facts. The Biblical archeologists look at the findings, and make it to fit the Biblical words & dates. The scientific one will make his own story out of the facts found on the site (by himself and by others).