Essentially I agree but how do you differentiate then between an atheist and an agnostic? It seems to me that to just say we can't know whether god exists or not, (agnostic), is not the same as believing that there is no god, (atheist).
This is actually a good question and a common misconception when people use the terms.
To provide a little more breadth to the discussion, theism/atheism and gnosticism/agnosticism are actually conveying different things. Theism and atheism talk about 'belief' while gnosticism/agnosticism actually speak about 'knowledge'.
For for example: an individual may ask someone the following question: "Do you believe in bigfoot?" The person may respond and say 'yes'. Then they are asked a followup question: "Are you certain bigfoot exists?" The individual may now respond 'No'. What is essentially occurring is that two questions are posited: one asking about the belief in a thing and the other asking about knowledge of a thing. Both yielded different answers.
So from the belief/knowledge standpoint, in the above example, this individual is indicating they have a belief in something, but not necessarily stipulating absolute certainty.
Now if we move over to the question of god, the style of questions are still the same. One can 'believe' in god but not be entirely certain. One can also not believe in god and also not be entirely certain. Both are displaying an 'agnostic' view on the knowledge portion but stipulating different answers to the belief question.
To itemize, as it pertains to the discussion on god, you can basically classify individuals into the following brackets:
Gnostic Theist - Believes in god and is absolutely certain he exists
Agnostic Theist - Believes in god but is not entirely certain he exists
Gnostic Atheist - Does not believe in god and is absolutely certain he does not exist
Agnostic Atheist - Does not believe in god but is not absolutely certain that he does not exist
(Note I left out the Deism view in this case, but the that is adding a third parameter to the question)
People often think that atheist and agnosticism are mutually exclusive when in fact, they are not. They are different responses to different questions.