It is easy to equate the two terms, but there is quite a bit of qualifying factors contribute to truth that do not for reality.
True and False
As children, we understand truth as something that is the opposite of false. But as we get older, our understanding of the word matures. Truths has a much deeper reservoir then originally thought. It is that ultimate reality. That ideal world we all long for, but may not all see.
Beginning with reality, a mathematically analogy could be appropriate here. See, real numbers include anything on the number line, in any direction. But whole numbers, conversely, must be on the positive side of the number line. And beyond that, natural numbers further quality whole numbers, excluding zero from the category. So reality is the outer circle, clarifying all things that exist as being actually real. But just because something is real doesn’t mean it is true.
Defining truth then presupposes reality, because things outside of reality are lack the quality of substance. They are contradicted by the category they exist in. Truth is then something that is exists correctly. It is something that is functioning properly. To further define the word, the inverse will give more perspective. Something that is false breaks the system. A solution that is false in an equation does not work. It is rejected. Something that is false is destructive. But it can still exist in reality. There is, in fact, many things in reality that are false, and they are eye sores, to be sure.
Is there anything that exists outside of reality, you ask? Well, it is a difficult question for me. Because I exist in reality, some trying to define something outside of my existence is not easy. I would have to describe it by the opposite of what I know is reality. We know of what we call “virtual reality”. This ussually implies some kind of googles, neural implants, or perhaps a dream state. But while the perception is very close to real from our perception, it is really just our brain being deceived of a false solution in reality. If virtual reality is happening, then our brain is not able to orient itself as to what is real, because it is looking for empirical evidences inside the virtual reality.
A Specific Solution
Reality then is quite extensive. And so it simply isn’t enough to pursue reality, because to be honest, it’s pretty hard to escape! But complex equations can be made that can hold a wrong variable very well. But looking at the equation as a whole, it is quite apparent that the equation is not functioning correctly without a correct solution.