When I moved to Colorado, it surprised me to see that the 'low grade' gasoline was 85 octane, where it was 87 in most other places. My vehicle's owners manual said to use 87 or above, so I thought I had to use "mid-grade", which was, well, 87 octane. But, then I started hearing rumors that "85 in Colorado is the same as 87 at sea level", so I decided to investigate further.
Side note: in the US, we use the (R+M)/2 method of determining octane values, which is different than other countries. So the typical 85/87/91 octane in Colorado may seem low, but they are not as bad as it might seem at first glance. I don't know much about the computation methods, so I won't go into detail here.
A quick tutorial on the relevant parts of how a gasoline engine works.. First, a piston in a cylinder moves down, creating a vacuum in that cylinder. The fuel/air mixture is sucked into the cylinder via an open 'intake valve(s)'. Then the intake valve(s) closes, and the piston moves up in the cylinder, compressing the fuel/air mixture (note: which also heats it up). Then, at the proper moment, a spark plug fires which ignites the compressed fuel/air mixture, which forces the piston down. The piston then moves back up, forcing the exhaust out the now open exhaust valve(s).
So, what is Octane? Answer: it is a knock inhibitor. What is knock? Knock is that 'pinging' noise you sometimes hear in some cars when accelerating. What is happening is that the fuel/air mixture in the engine's cylinders is actually igniting before the spark plug fires. Another name is preignition. Basically, the fuel/air mixture is getting to a high enough temperature due to the compression of the fuel/air in the cylinder to ignite on its own. Octane increases the ignition temperature, making it such that it is less likely to ignite until the spark plug fires.
Thus, higher octane implies 'higher ignition temperature' or 'higher flash point'.
This explains why many sports cars and high-end cars require high octane fuel. Cars that have high compression ratio engines must in-turn require high octane fuel. The more an engine compresses the fuel/air mixture, the higher the temperature gets inside the cylinders, and in-turn the more prone to pre-ignition/knock.
So, why does Colorado have lower octane fuel available? Answer: the altitude. At 5,000 feet, there is less air available to the engine. There being less fuel/air to compress in the cylinder means that the temperature does not get as high in the engine's cylinders, thus not as much octane is required. For driving in the mountains where the elevation is even higher, one actually needs lower octane.
Why is it called premium? Beats me. All reputable refineries put the same detergents and additives in all of their grades. The only difference is octane. There is nothing "premium" about it as far as I can tell. If you don't need it, you won't get any benefit. The recommendation I've heard most often is to go by the recommended octane level as specified in your vehicles owner's manual. If you live at 5,000 feet, you can safely subtract 2 from that recommended value. You can tell if you go too low, as you will start to hear your engine knocking or pinging. If you do, simply move up a grade. If you never hear knock, there is no reason to move up a grade.
Why don't diesels have grades? Diesels work slightly differently from gasoline engines. A gasoline engine sucks in a fuel/air mixture, then compresses it, then a spark plug fires to ignite it. A diesel sucks in air (with no chance of pre-ignition), compresses the air (which also heats it), then injects the fuel into the already compressed cylinder. The air is hot enough and diesel fuel has a low enough ignition point that it now ignites. That's also explains why many diesels have "glow plugs", they are there to warm the cylinders before the engine has had time to warm up to normal operating temperature.
My understanding is that modern engine control computers are constantly tuning an engine as they drive. They also sort of remember what seems to work best. So, it is best to always use the same brand and octane of gasoline each fill-up. If you do switch, it may take a few tanks for your vehicles computer to adjust the engine to work optimally with the new gasoline. Have you heard the ads "try us for 5 tanks"? Now you know why... This data could be out of date, modern vehicle computers may adjust more quickly to changes. I just don't know.