Are "sin" and "transgression" different in LDS terminology?

Throughout the history of the Church the two terms have been used both interchangeably and independently with such inconsistency that it often confuses people sitting in Sunday School today.

Most of the confusion comes from a desire to ameliorate the opinion people have had toward Adam and Eve over the last 2,000 years. It's understandable as, for example, a great portion of western culture's misogyny can arguably be blamed on Christianity's unhappiness over Eve biting the apple first.¹ (Personally, I don't worry about it. I have enough trouble with the beam in my own eye.)

However, in reality, there is no difference whatsoever. Here's the scripture chain...

For I the Lord cannot look upon sin with the least degree of allowance; (D&C 1:31; see also Alma 45:16).

Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law. (1 John 3:4)

We believe in being subject to kings, presidents, rulers, and magistrates, in obeying, honoring, and sustaining the law. (AoF 1:12)

Let no man break the laws of the land, for he that keepeth the laws of God hath no need to break the laws of the land. Wherefore, be subject to the powers that be, until he reigns whose right it is to reign, and subdues all enemies under his feet. (D&C 58:21-22)

And again, verily I say unto you, that which is governed by law is also preserved by law and perfected and sanctified by the same. That which breaketh a law, and abideth not by law, but seeketh to become a law unto itself, and willeth to abide in sin, and altogether abideth in sin, cannot be sanctified by law, neither by mercy, justice, nor judgment. Therefore, they must remain filthy still. (D&C 88:34-35)

The consequence: Driving above the posted speed limit is a sin that will keep one out of heaven.

The vast, vast, vast majority of Church members don't believe what I just said... but who are we to make God in our own image? A fair number of Church leaders have taught that we must obey the laws of the land.² The command to be perfect is a harsh taskmaster (and I have a long way to go).

_{¹ The rest of it is thanks to Paul the Apostle's general distaste for women. Between the two, treating women as the equals they are became a hard sell.}

_{² In regard to the quote from Elder Oaks cited by DougVj, please note that the last sentence is unbelievably important. "These words are not always used to denote something different, but this distinction seems meaningful in the circumstances of the Fall." I have only ever heard a distinction in regard to the Fall of Adam and Eve — and I do not have evidence that it is official doctrine even then.}

The two terms are often used interchangeably, in line with John's declaration that "sin is the transgression of the law." (1 John 3:4) However, there is at least one significant point in LDS doctrine where the two terms are treated as distinct.

The second Article of Faith states:

We believe that men will be punished for their own sins, and not for Adam’s transgression.

LDS theology does not recognize the concept of "Original Sin" as it is generally understood in other Christian denominations, the idea that the Fall causes all mankind to be inherently sinful and inherit guilt and condemnation from Adam's actions. The Fall of Adam is understood to be a transgression of God's law, but not an inherently sinful act, as it was a part of God's plan: in order for God's children to progress, they had to live in an imperfect environment where they would be subject to temptation, that they could learn the difference between good and evil for themselves, and learn to live by faith, and choose good and reject evil.

One of the implications of this doctrine is that, as all men are accountable only for their own personal sins, and not for the acts of Adam or anyone else, this means that children are born in a state of innocence and do not require baptism for the removal of the guilt of Original Sin. Moroni chapter 8 from the Book of Mormon lays out this doctrine in clear (and fairly strong) words.

Yes they do have different meanings, though not consistently. Joseph Fielding Smith declared about the fall:

I never speak of the part Eve took in this fall as a sin, nor do I accuse Adam of a sin. … This was a transgression of the law, but not a sin … for it was something that Adam and Eve had to do!

-Joseph Fielding Smith, Doctrines of Salvation, comp. Bruce R. McConkie, 3 vols., Salt Lake City: Bookcraft, 1954–56, 1:114–15

Dallin H Oaks, referring to the above quote, said:

This suggested contrast between a sin and a transgression reminds us of the careful wording in the second article of faith: “We believe that men will be punished for their own sins, and not for Adam’s transgression”. It also echoes a familiar distinction in the law. Some acts, like murder, are crimes because they are inherently wrong. Other acts, like operating without a license, are crimes only because they are legally prohibited. Under these distinctions, the act that produced the Fall was not a sin—inherently wrong—but a transgression—wrong because it was formally prohibited. These words are not always used to denote something different, but this distinction seems meaningful in the circumstances of the Fall.

-http://www.lds.org/ensign/1993/11/the-great-plan-of-happiness

Further, It has been said that Adam and Eve merely transgressed the law because they did not yet know the difference between good and evil, and thus they were not accountable for sin. A similar argument is used to say that children cannot sin; they are not accountable. They do, however, trangress laws.

The distinction between the two terms is not always clear cut though and invariably the two will be used interchangeably despite the subtle difference.