Strange to think: If you tell someone that there is a difference between reading books about playing the piano and actually playing the piano, most would agree like a shot; it would be a d'oh observation.
But if you tell someone that there is a difference between an intellectual or emotional approach to Buddhism and the experience that Buddhism invites, right away there is a segue back to intellectual or emotional appreciations ... sort of like a dog chasing its tail. It's not naughty or bad, it just seems to be what happens.
Buddhism, in a nutshell, makes observations about the world we live in (The Four Noble Truths) and then, assuming anyone finds those observations useful or appropriate, it makes suggestions about the best ways to put those observations to work (The Eightfold Path). To extend the piano analogy, it's as if someone told you, "This is a piano. It makes beautiful music." And if you wanted to create beautiful music, there would be instructions on how to play this piano. Whether anyone follows those instructions or not is entirely up to them ... do they want to make some effort or do they simply want to talk? Do they want the theory or do they want the experience?
Imagining that the experience of playing the piano could be adequately captured in words would be a fool's errand.
But the fact is that we are all fools to start out. It's just the way we have been brought up. It's our habit. Not better or worse ... just a habit. But when we find that past habits don't really succeed in providing a peaceful and contented experience (a beautiful music), then at last there may be some willingness to make some actual-factual effort.
When it comes to the matter that Buddhists sometimes call "enlightenment" or "enlightened beings," these are just tentative references to what beautiful music might be. But no one in their right mind confuses "beautiful music" with beautiful music. The notion that someone else might be enlightened is just a way of inviting a personal effort ... to make their own beautiful music.
To the intellectual and emotional way of thinking, there are a lot of variations on beautiful music. Mozart, Beethoven, Brahms ... the list goes on and on. But as a matter of experience, there is only this beautiful music, this moment, this enlightenment. There is no escaping beautiful music ... but as a matter of encouragement and inspiration, we speak in a variety of ways of that which is neither various nor singular ... the experience of beautiful music.
Sorry for all the blither.
1) What do the various representations of enlightened figures tell us about how Buddhists perceive the ideal of enlightenment?
The representations are just ways of pointing out capacities and misperceptions that anyone might experience. They are, like all spiritual endeavor, advertising.
2) Why is there so much variation?
The intellectual and emotional mind sees many variations, but, as appicchato points out, this just relates to human nature. Human beings aren't lock-step clones looking for a cookie-cutter religion ... they are wide open as the sky, looking for beautiful music in infinite ways. If human beings cannot be boxed, why would Buddhism attempt to box them? Buddhism is as if we went to a restaurant: You order eggs, I order spaghetti ... it's not a matter of better and worse since both of us receive nourishment. Nourishment is just another form of beautiful music.
3) What uses might these representations be put to?
Such representations are only as useful as whatever effort you might be willing to expend. Buddhism isn't in the adoration business. It isn't into the limitations that the intellect provides. It is in the experience business. Anyone can worship or adore a piano (or the intellect), but in order to make your own beautiful music, practice, and the experience it brings with it, is probably more sensible. Experience trumps explanations and belief and it is practice that provides experience. So in one sense, the representations of 'enlightened' beings encourage and inspire us, but as a matter of experience, they are utterly useless. No one who knows how to play the piano worries about whether someone else plays the piano. S/he just plays and makes beautiful music.
Sorry for so much talk. I hope some of it is useful.