People disagree about the meaning and usage of these terms. People frequently claim that an atheist is completely certain in his/her own mind that God does not exist. The following explanation is presented to clarify these terms in common usage. People in different English speaking countries use the words atheist and agnostic in slightly different ways.
People sometimes say stuff like, “I’m an agnostic” when the other person thinks they’re closer to a weak atheist. Alternatively people call themselves atheists while others think they’re agnostics. Then people can get accused of lying when they didn’t intend to deceive anyone. Below are examples of different use of atheist and agnostic:- Richard Dawkins argues that there almost certainly is no god and is considered an atheist. Bertrand Russell also believed that god is very unlikely but called himself an agnostic at least part of the time,  .
People generally hate it if they get called liars despite trying to be honest. So at the very least we should take care to remember that other people may use these two words with a different meaning from the meaning we assume.
Proving a negative
It's very difficult to prove a negative and Strong atheism is hard to defend. I can't prove that there are no Fairies, elves, goblins or other supernatural beings in the parkland near my front door for example but is it likely?
See Proof God Doesn't Exist! for more.
One common tactic of Christian apologists is to demonstrate to an atheist that he/she can't exclude a remote possibility that some type of god exists and then declare triumphantly, "there you are! You see you're not an atheist, you're an agnostic." The typical follow up from that is using Pascal's Wager to try and get the atheist/agnostic really frightened. For why Pascal's Wager doesn't work see the article.
- We should be careful not to assume the difference between atheist and agnostic matters more than it does.
- It doesn't matter over much whether other people call themselves atheists or agnostics.
- It doesn't matter over much whether other people call us atheists or agnostics.
Theism is about belief in a god or gods. For any claim about the existence of a god or gods, theists accept that this claim is true. One way of stating this is that theists have the positive belief that the god claim is true.
Atheism literally means "without theism". An atheist is someone who does not accept, as true, claims that assert the existence of gods.
Considering the claims regarding the existence of a god, there are two possible claims:
- God exists
- God does not exist
For either claim, there are two positions one can take with regard to belief:
- belief or acceptance of the claim
- disbelief or rejection of the claim
For claim number 1 (God exists), the theist's position is one of belief, while the atheist's position is one of disbelief.
For claim number 2 (God does not exist), the theist's position is one of disbelief, while atheists can hold either position.
Some atheists actively believe that no god exists while others hold that neither claim is sufficiently supported to justify acceptance. These positions are often labeled strong atheism and weak atheism, respectively. Additionally, some individuals confuse the weak atheism position with agnosticism. There isn't much difference between weak atheists and agnostics. Agnostics are more likely to feel positive about the possibility that God or a higher power might exist. Weak atheists are more likely to believe that God is improbable and weak atheists focus on living life as if there certainly were no God. Weak atheists are likely to argue that if god/gods exist we can't know what they want from us so we might as well live our lives taking only this world into account. 
Gnosticism (in the sense used here) addresses the issue of what one knows or claims to know. For any claim about the existence of god, gnostics are individuals who claim to know that the claim is true. Typically, this claim of knowledge is esoteric and may be attributed to divine revelation. In some cases, the gnostic will assert that this knowledge is available to anyone though rarely through empirical, scientific evidence.
An agnostic is, literally, someone who does not claim to know that such claims are true. An additional, and common, usage of the term agnostic exists as a label for the philosophical position invented by Thomas Huxley. Those individuals adopting this label claim that the answers to questions about the existence of gods are unknown and unknowable. Additionally, many claim that the questions are essentially meaningless as "god" is ill-defined. (See theological noncognitivism and ignosticism.)
Notice that the terms "atheist" and "agnostic", by these definitions, are not mutually exclusive. You could be an agnostic atheist, meaning you don't think one can know whether or not a god exists, but you don't feel that belief is justified by evidence or argument.
Many people assume that atheists believe that gods can be proved not to exist, but this isn't strictly true and there is no word to describe this. You could call such a person an "untheist" or "antitheist", perhaps. Or, you could just call such a person a "gnostic atheist", one who doesn't believe in a god and thinks that his belief can be proven.
As the terms aren't mutually exclusive, it's possible to combine them into four descriptions:
|Atheist||1. Agnostic-Atheist:does not believe any god exists, but doesn't claim to know whether this is actually true||2. Gnostic-Atheist:believes that no god exists and claims to know that this belief is true|
|Theist||3. Agnostic-Theist:believes a god exists, but doesn't claim to know that this belief is true||4. Gnostic-Theist:believes a god exists and claims to know that this belief is true|
It's important to note, when discussing the complicated issues of knowledge and Epistemology, that these claims of knowledge do not necessarily require absolute omniscience. It can be argued that we can never truly "know" anything (see Wikipedia:Agnosticism), yet we constantly make claims of knowledge — you may "know" who your (birth) mother is, for example, but you could be wrong. For many gnostic atheists (strong atheists), their claim of knowledge stems from practical considerations. The positive assertion that "gods don't exist" can be made, and said to be "known", in the same spirit as the statement that "leprechauns don't exist".
- Definition of Atheism Cambridge University in the UK tries to define atheism and uses the term, "negative atheist" where others might say, "weak atheist" or, "weak agnostic".
Neither atheism nor agnosticism implies any position on morality though both atheists and agnostics are likely to reject moral systems based on so-called revealed texts like Christian morality. Among many western atheists and agnostics Humanist morality is popular.