I always have understood "sin" to be different than "transgression". "Transgression" is the broad, umbrella category of "going beyond or overstepping some boundary or limit" - in religious terms, of breaking a commandment. "Sin", otoh, is a subset of transgression where one understands a commandment and consciously chooses to break it. Therefore, a young child can transgress without sinning; a Catholic can transgress the Word of Wisdom without sinning; my retarded cousin can transgress without sinning; etc.
At the most basic level, every person transgresses and every person who is capable of understanding the validity of a limit / law / commandment sins. We all do things we know we shouldn't do, and we all don't do things we know we should do. The trick, imo, is knowing what things we really are capable of doing - so we know what constitutes sin for ourselves as individuals.
The best example, again, is my retarded cousin - or someone with severe dementia. Some things that are sin for me are transgressions for him. However, most (if not all) of us are not fully aware of our own "hidden disabilities" - so we are not fully aware of what actually is within our control and what is not. Therefore, all we can do is our best to understand ourselves and strive to develop the characteristics of godliness that will eliminate our weaknesses that cause our sins and transgressions.
We have been told that we will not be punished for the natural transgressions we commit simply as a result of the Fall (our actions we don't consciously choose, like the words my friend utters in the throes of her bi-polar disorder or my mom's actions when her "sleeping pills" no longer worked), as a reward for the pre-existent choice we made to accept Jehovah as our Lord and Savior and Redeemer. (Iow, we won't end up worse off as a result of our birth than we would have if we had never been born.) We also are told that our sins (incorrect *choices*) can be forgiven *as long as we accept the Lord's redemption and strive to become like Him and our Father*. The promised forgiveness of our transgressions gave us access to a degree of glory; the offered forgiveness of our sins gives us hope for a fullness of glory. The first (forgiveness of transgression) places us above Lucifer and his followers; the second (forgiveness of sin) opens the possibility of being a joint-heir with Christ.
I believe the Restored Gospel we currently teach broadens the gray and shrinks the black and white dramatically - particularly compared to most Protestant denominations. The black and white still exist, but most of us live and learn and struggle in the gray - forever fighting to see and understand and live correctly whatever constitutes the "true" black and white. I believe our church more clearly defines the ultimate objective FAR better than any other of which I am aware and gives us access to more light and knowledge than any other of which I am aware, but I also believe we still "see through a [grayish] glass darkly" - much more than many "black-and-white-ists" believe.
My concern over the distinction comes from seeing so many people who feel "guilty" for their naturally inherited weakness - the things that lead them to transgress - as if they were sinning simply because they couldn't overcome totally that inherited weakness. They have been told so often that "any mistake is sin" that they beat themselves up continually over what amounts simply to being human. They can't recognize that Jesus already has paid that price for them - that "the truth will make you free" in that particular way - that they can "cast those burdens at His feet" and simply look for ways to change without debilitating guilt over how hard it is and how long it takes.