Prior to reading Langston Hughes Salvation, I defined sin as something that you have done wrong. But, in reading Langston Hughes essay, it used sin to mean something like not believing in god. So, my question is whether sin means the first, second or both of the definitions.
The short answer to your question is both.
- a. an offense against religious or moral law
- b. an action that is or is felt to be highly reprehensible
- c. an often serious shortcoming : fault
If not believing in a god is a violation of a religion's law, then in the eyes of that religion the act of not believing is sin. In this sense, your second example would actually fall under your first umbrella. However, the exact list of what constitutes sin will vary between belief systems/religions, so what one group/individual may view as sin may not be seen as sin by another group/individual.
Apart from religious connotations, definition 1b that I quoted above is probably the most likely/reasonable definition.
In religion, sin is a concept not only of doing something wrong (and doing something wrong includes not believing in the right ideas) but also condemned state. Someone who has committed a sin is in a state of carrying sin, like a dirty stain, which can be "washed away" when God forgives. In Christianity there is also the concept of "original sin": carrying sin from birth, having done nothing wrong (or nothing at all, really).
So sin is a word which denotes both the offense and the "criminal record", so to speak.
There is no difference between your two definitions: not believing in God is doing something wrong, among those who believe in that type of religion and use use sin in its context.
You're only disagreeing that simply not believing in something is doing something wrong; but that is irrelevant to the definition of sin. Two people don't have to agree on what is sinful in order to agree on the definition of the word "sin".
A secular use of the word sin is to denote something which is irrationally wrong due to offending someone's preferences or tastes, or whatever:
Did you hear? Jack committed the grave sin of making fun of golf within earshot of the vice president. He can pretty much kiss that promotion goodbye!
Example from a technical context in the field of computing:
Assignment to variables is considered a sin by adherents of pure functional programming, and so they invent and use languages in which it isn't possible.
Langston Hughes is not a theologian. He may qualify as a philosopher, or even as a pretty smart guy, but I seriously doubt that he's the final arbiter on the definition of sin.
I think SnoringFrog has a good case: that there's a religious definition of sin, and a secular one. If it were only religious, it would be a meaningless concept for atheists.
One religious definition of sin is that it is a moral evil. So now we have to figure out what "moral" and "evil" mean. "Evil" is a complicated subject, but we can simplify to the basics as "that which harms". Murder is evil; theft is evil; lying is evil. I believe that there are degrees of evil; the Holocaust is one of the greatest evils; lying in order to have your little sister get the blame for something you did is a lesser evil. Lying to protect someone from harm (as in, during the German Reich, saying, "No, there are no Jews here") is usually good.
"Moral" is also a wide concept. Almost every society has (or had) some concept of morality - there are things that are OK, and things that are taboo. Those concepts vary widely, and unfortunately, we have fallen victim to the error of "moral relativity": the idea that whatever society A holds a moral, is OK.
You can learn a lot more by reading C. S. Lewis, for example, "The Abolition of Man". (Read the non-fiction books first.) One thing that comes out of Lewis' book is that there are concepts of good that are common to almost every religion and philosophy. Confucianism, for example, says "Do not do to others what you would not have them do to you".