This is a topic that was hotly discussed at one time, but not so much currently. The fact is that different fishes and inverts have different tolerances. Some marine environments tend to be SLIGHTLY more saline than average because of high equatorial evaporation rates coupled with an lack of FW intrusion. The Red Sea is an example. Other areas are less saline due to the presence of rivers, melting ice, etc. Coral reefs tend to be very consistent and stable, with S.G. averaging about 1.025. The most delicate corals will have no problems with small deviations from that, to 1.026 or 1.024. Hardier corals shrug off even greater variations.
Fish are slightly different. Those species that live in stable salinities and temps may be less adaptable than other fishes, but all of them can adapt to lower salinity. They can handle higher salinity as well, but this places a physiological strain on them. SW fish are constantly excreting salt in order to maintain their osmotic balance. The saltier their environment, the greater the strain on their body. It should be noted that the oceans are slowly, over the course of millions of years, becoming saltier. The ancestors of our present fish swam in less saline seas. I have read some interesting speculation regarding very early human evolution and our blood salinity levels.
Most SW aquarium fish do well from 1.020 to 1.028. Some aquarists keep fish at low salinities, to reduce the physical strain on fish, and also because it is less expensive. This seems to work well for MOST fishes, but I don't recommed it except for those fish that are found in estuaries and bays, like boxfish, puffers, trunkfish, seahorses, lookdowns, etc. Some dealers jack up the salt level because this is said to make the fish more active and a touch more vivid. Not a good idea, I think.
I keep my fish-only aquariums at about 1.022 to 1.023, and my inverts and mixed aquariums at 1.024 to 1.025. I'm sure I can get away with wider variations, but those are my optimal settings. Needless to say, any changes should be made gradually. Also get a GOOD hydrometer, and make sure you know how it is temperature adjusted. I personally don't like those plastic gizmos with a pointer inside. Get a real hydrometer, and check to see at what temp it is regulated. Many are set at 68F. If your aquarium is 78F, a reading of 1.023 on that hydrometer means your water is really around 1.025.