What is a natural area and what is a rural area?
Natural areas tend to be those regions that are either protected from human activities or been lucky enough to not have had a huge human impact as yet. Rural tends to be regions that have been cleared of trees for farming.
There is no hard and fast definition between these two terms, but the aforementioned captures the differences pretty well. Some farmland is sometimes turned back into a "natural area" in which limited or no human activities are allowed.