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.