The vocabulary of belief and disbelief in God is often used as though it named points along a single line running from certainty that God exists to certainty that God does not. The more useful analysis, now standard in philosophy of religion, separates two questions: what a person believes, and what a person claims to know.
Theism and atheism answer the first. Gnosticism and agnosticism, in this technical usage, answer the second. The two axes are independent, which is why the combinations are the interesting part: a person may be an agnostic theist, believing without claiming knowledge, or an agnostic atheist, not believing while making no claim to know there is nothing to believe in.
The terms carry histories that complicate them. "Atheist" was for most of its life an accusation rather than a self-description: it was levelled at Socrates, at early Christians who refused the civic gods, and generally at anyone whose theology was sufficiently unlike the accuser's. Self-described atheism becomes common in Europe only in the eighteenth century. "Agnostic" was coined by T. H. Huxley in 1869, and coined deliberately to name a principle, that one should not claim certainty where the evidence does not warrant it, rather than a doctrine about God; Huxley presented it as a method, not a creed.
"Atheism" is also defined differently by different parties, and a great deal of unproductive argument turns on this. On one definition it is the positive claim that there is no God, which carries a burden of proof. On another it is simply the absence of belief, which its holders argue carries none. Neither definition is incorrect, and disputes about who must prove what are frequently disputes about which definition is in play.