The terms ‘atheist’ and ‘agnostic’ are not mutually-exclusive. ‘Agnostic’ is a term that can be applied to many different philosophical positions. ‘Atheist’ is a term about a very specific position – that is, the belief in the existence of a god.
A lot of people think that the word ‘atheist’ means someone who believes that god doesn’t exist, and that the word ‘agnostic’ means someone who is undecided. This is not correct.
The word ‘atheist’ means someone who does not believe that any gods exist – this includes both people who believe that no gods exist (known as positive atheism), and people who simply don’t believe that any gods exist (i.e., they are simply not convinced that any gods do exist – known as negative atheism).
The word ‘agnostic’ means someone who does not claim to have knowledge of something. This can be seen in the etymology of the word. The word ‘agnostic’ comes from Greek a, meaning ‘without’, and gnostos, meaning ‘knowing’. You can be agnostic about many different things. For example: how many tins of tomato soup are there at your nearest supermarket? Are there 20? 30? 50? 100? You don’t know. You might be able to make a reasonable guess – say, more than 25 – but you wouldn’t claim to know unless you’d gone there and counted them. You wouldn’t believe, or have conviction, that there were, say, 17 – because you had no proof.
For this reason, negative atheism is often called agnostic atheism. Negative atheism is the position that you have no proof that any gods exist, so you’re not going to believe that any do, but you’re not going to believe that any don’t either. Positive atheism, by contrast, is often called gnostic atheism – where gnosticism is the opposite of agnosticism. Gnostic atheists claim to know, for certain, that there are no gods. (Very few atheists are gnostic atheists – it is generally considered to be an irrational position by most atheists (though it depends on the definition of ‘god’).)