The strong-atheist actively disbelieves in a God. s/he has considered the question of whether or not there is a God or gods, and has answered the question "no".
The weak-atheist passively disbelieves in a God. s/he has heard the question of whether or not there is a God and refuses to answer because no available evidence exists in either direction. The question itself is meaningless.
In practice, agnosticism and weak-atheism are identical and strong-atheism is often translated as just atheism when the two are mentioned together. The agnostic does not trust conclusions that are not based on empirical evidence and/or logic. Thomas Huxley, who coined the modern-day term "agnostic" in 1869, has this to say.
In terms of everyday life, both agnostics and atheists behave as if there were not a God or gods. But the agnostic tends to consider the various questions posed by religion and judge them on their merits, while the atheist tends to reject religious doctrine outright as it applies to invisible deities.Agnosticism is not a creed but a method, the essence of which lies in vigorous application of a single principle. Positively the principle may be expressed as: in matters of intellect, follow your reason as far as it can carry you without other considerations. And negatively, in matters of the intellect, do not pretend the conclusions are certain that are not demonstrated or demonstrable. It is wrong for a man to say he is certain of the objective truth of a proposition unless he can produce evidence which logically justifies that certainty. That is what Agnosticism asserts; and, in my opinion, it is all that is essential to Agnosticism. ... The application of the principle results in the denial of, or the suspension of judgment concerning, a number of propositions respecting which our contemporary ecclesiastical "gnostics" profess entire certainty.
There are also shades of in-betweenness, but this seems like a good place to start. Where do your values fall? And what are your views concerning "proofs" of God, Heaven, etc.?