Mad implies insanity, but people these days think anything they wouldn't do is insane. They are words, nothing more - and as always, are subject to their common usage and acceptance in society.
You used to have to be insane to admit you were gay. And now people do it all the time. People in Oblivion call you "mad" or insane when you murder someone, but people in real life who commit murder 90% of the time are poor, stupid fools who can't hardly hold down a job. That doesn't make them insane, it just makes them an idiot. And they get caught, and spend the rest of their lives in jail for some stupid mistake.
"Mad" as we know it, does not mean insane, as we gamers envision it. Technically "insanity" isn't even a psychologically accepted term. It is a legal term, and when used as a defense in court, almost always fails. In psychology, you are not insane, you have a mental illness - a specific mental illness, that in order to be specified, has to meet very specific requirements. Most of the time these requirements are simple labels such as "Poses a danger to themselves or others" or "Continued behavior that is not socially acceptable." (Along with several other, more specific qualifications.)
But again, these qualifications don't necessarily mean "insane" or crazy vaporized floating backwards staircases and episodes of mania.
A good portion of the time, they just mean "other than the norm". Or quite frequently "Idiotic."
Both of which can be found in excess, in the Shivering Isles.
It is also worth noting, that as the Mad God, lore and books seem to point to Sheogorath's love for screwing with people, fellow daedric princes, everyone. And if his realm was truly "insane" as you would like to see it, people would flat out not exist or be able to coincide. His realm follows his personality, while consequently allowing for the personalities and existances of his followers and as a result, partial "entertainment". Read some books about his playing with people's minds and fooling daedric princes, and you'll have even more reasons as to why his realm exists as it does.
that just about hits the nail on the head right there. the technical def of "mad" is some form of insanity and is not linked to a particular emotion as we so often use it to mean. You might also want to remember that insanity, or madness, is not always so easy to spot. An insane, or mad person could look and act totally fine, until you talk to them that is. Such is the instance of Sheogorath. He looks like a relatively harmless old man sitting on his throne, until you talk to him that is... and as Two said, a person could be characterized as insane just because they do something out of the ordinary. That argonian that is always running around comes to mind, or how about that Khajiit in, I believe "Things Found" that has you collect those odd objects for the "end of the world", or how about that guy that is always cowering, claiming that the walls are going to fall on him? Those individuals would be characterized as insane because they act different than what is considered socially acceptable. Why, i think the only sane individuals in the entire realm besides you are the dark seducers and golden saints. At least i havnt seen them do anything odd...