"Secular Humanist" Humanism holds that the universe exists for no purpose. We are the result of a blind and random process that does not necessitate any kind of meaning. Humanism differs from the more extreme philosophy of nihilism, in that life can have a meaning if we assign a meaning to it. Life is only worth living if we ourselves make it worthwhile and enjoyable. Humanism maintains that no objective or universal values exist. A person may be moral if he or she creates a system of values and lives according them. A humanist would maintain that no one is obligated to be moral. Therefore, humanism fails to provide moral objections to immoral behavior. Obviously, if no moral absolutes exist, you can't demonstrate that anything is wrong or evil. Thus, in a humanist society, no one can really judge or condemn the choices or actions of others.
"Non-Religious" The worldview of nonreligious people simply don't have the major conceptual elements found in the worldview derived from any religion. A nonreligious framework for human living is void of any divine entity or deity’s involvement in human life or of considerations of existence after death. Perspectives on morality are likewise naturalistic.
"Theism" Theism is, literally, belief in the existence of God. Though the concept seems to be as old as philosophy, the term itself appears to be of relatively recent origin. Some have suggested that it appeared in the seventeenth century in England to take the place of such words as "deism" and "deistic" when referring to belief in God. "Theism" is often used as the opposite of "atheism," the term for denial of the existence of God, and distinguishes a theist from an atheist or agnostic without attempting any technical philosophical or theological connection. The term is also used as a label for religious believers, though again, there is no attempt to imply a particular theological or philosophical position. Finally, the term is used to denote certain philosophical or theological positions, regardless of whether this involves a religious relationship to the God of whom individuals speak.
"Agnostic" The English term "agnostic" is derived from the Greek "agnostos," which means, "to not know." An agnostic is one who admits, "I don't know." The term is applied specifically to those who don't know for certain whether or not God exists. An agnostic is one who believes that the existence of God is unknown and most likely beyond human ability to discover.
By definition, an agnostic is not committed to believing in or disbelieving in the existence of God. Nevertheless, while agnosticism claims to "sit on the fence," many agnostics are "practical atheists," in that they actively pursue the atheistic lifestyle; that is, they tend to subscribe to moral relativism and live out their lives without any concern for ultimate accountability.
"Atheism" Atheism is characterized by an absence of belief in the existence of gods. This absence of belief generally comes about either through deliberate choice, or from an inherent inability to believe religious teachings which seem literally incredible. It is not a lack of belief born out of simple ignorance of religious teachings.
Some atheists go beyond a mere absence of belief in gods: they actively believe that particular gods, or all gods, do not exist. Just lacking belief in Gods is often referred to as the "weak atheist" position; whereas believing that gods do not (or cannot) exist is known as "strong atheism."
Regarding people who have never been exposed to the concept of 'god': Whether they are 'atheists' or not is a matter of debate. Since you're unlikely to meet anyone who has never encountered religion, it's not a very important debate...
It is important, however, to note the difference between the strong and weak atheist positions. "Weak atheism" is simple skepticism; disbelief in the existence of God. "Strong atheism" is an explicitly held belief that God does not exist. Please do not fall into the trap of assuming that all atheists are "strong atheists." There is a qualitative difference in the "strong" and "weak" positions; it's not just a matter of degree.
Some atheists believe in the nonexistence of all Gods; others limit their atheism to specific Gods, such as the Christian God, rather than making flat-out denials.