Oh. I guess I should write a little bit more than that, huh. Well, let's see... Reality isn't something that can be changed or altered by perception, because reality IS reality. Truth is the same thing really, but truth is more often associated with people, or what people see as reality. So truth can be distorted by perception, whereas reality is always reality.
I kind of wrote a bit about this when blogging about 1984, and my position is more or less the same. There is an objective reality, but people can only perceive it in the mind, and who knows if the mind is right or wrong. If everybody says up is down and you have no frame of reference to disagree, then that is your truth - it isn't reality, in reality up is up, but because nothing is challenging you from thinking up is down, your mind has been deceived into accepting a false truth. I'm pretty sure this is what Plato was getting at, at least to an extent. The people in the cave only see what's directly in front of them as shadows, so for them, there is nothing but those shadows and the cave they're in. While those shadows and the cave are, in reality, there, the prisoners' perception is distorted because that is all they know - their truth is the cave and nothing more, when in reality there's obviously much, much more.
Plato's allegory is more concerned with the concept of philosophical thinking than really determining the difference between truth and reality, however. The prisoners represent the general population of the world, people that don't know the nature of the universe and don't really care to. The one who 'sees the light' is one who breaks free of that apathy and starts questioning and trying to discover reality, the the best of the human minds' ability. There's no real need to discover the relationship between truth and reality in the allegory, because the point (or, at least, the point I understood) is that while reality exists, we can only perceive it in the mind, and some of us spend lots of time on that kind of philosophical thinking while others are content with going only by what the see.
