Secularism is the separation of state and religion. Or in other words, not making laws that are dependent on someone’s religion (e.g. Sharia). It is the apple. An apple a day keeps the big bad religious extremists away.
Non-religious is not being associated or affiliated with religion. Like Iron. How religious is iron? Not in the least. When talking of humans, non-religious, or rather irreligious would mean someone who does not belong to any religion. They need not be atheists. They can be theists, deists, pantheists, etc. It is the iron. A basic element making up matter.
Agnostic is a position. That of not knowing if a god or gods exists. You can be agnostic theist, agnostic atheist, agnostic pantheist, agnostic deist, etc. Given the current lack of proofs for existence of, or against existence of god or gods, it is by far the most logical positions. It is the television with which you see the world, whether coloured, or B&W or HD and so forth. And it is made up of one or multiple of the elements, like Iron.
Atheist means someone who does not believe in any god, or someone who believes god does not exist. Both definitions work. First is logical, Second without proof is not. Its other counterparts are theists, deists, pantheists, etc. If these are the various television channels, then Atheism is the off television. The television exists, the element is there, but there is no channel playing.