Most fish are tolerant of only a limited variation in the saltiness of the water in which they reside.
However, different fish have different abilities to go from salt to freshwater or the other way around.
Some (like salmon) change their abilities to do this based on their stage of life. Salmon start in freshwater (as eggs), then go to the ocean, then return to freshwater to mate and lay eggs. Their physiology changes to make this possible.
Bull sharks are usually found in oceans but can go far up rivers.
Some fish have benefits from more or less salt. Slightly salty water is good for some larval fish at certain ages. It takes energy to pump excess salt out of their bodies, so adding a little salt (but not too much) to the water can benefit them.
Generally speaking, brackish fish (fish in water where fresh mixes with salt) probably have the largest tolerance. (there are some really interesting brackish fish to keep if you are a fish keeper, but as said above, they are more difficult.)
The major take home lesson would be to research what the specific kind of fish you are interested in can tolerate at what time in their life cycle.
There are many resources for this information: books, magazines, websites, extension services, aquaculture organization, hobbyist organizations.