The term theism is derived directly from the classical Greek word for god, so at a minimum being a theist requires that one be reasonably (but not necessarily absolutely) confident that at least one supernatural, conscious deity that either created humanity and/or is involved human affairs exists. Because a-theism merely means the absence of theism, anyone who is not a theist is automatically an atheist even if they don't like being tagged with the term. Because lots of atheists don't like being called the same, the number of atheists is often under realized, contributing to their second class minority status. The degree to which atheists are atheists varies tremendously. Coined by Thomas (Darwin's Bulldog) Huxley, agnosticism describes those who think the non/existence of any gods cannot be entirely determined based on the current evidence. That describes a big chunk of atheism. Absolutist atheists who have no doubt that there are no gods based on philosophical logic (as controversially proposed by Ayn Rand whose libertarian economics have become amazingly popular among theoconservatives; click here) are pretty scarce.
The term "new" atheism is not particularly descriptive of today's up and coming movement, it is more correctly assertive atheism. Even more inappropriate are the propagandistic "militant" or "fundamentalist" atheism. Fundamentalism means a perceived return to the fundamentals of something like scripture, none of that can apply to the absence of theism -- it is as abjectly impossible for an atheist to be a fundamentalist no matter how strident they may be any more than a person zealously opposing ghost belief can be an antighost fundamentalist. Nor are assertive atheists employing violence to further the cause the way actually militant Muslims, Hindus and Christians are fighting for their faith.
This highly skeptical albeit agnostic assertive atheist, by the way, often describes himself as an antisupernaturalist, or nonsupernaturalist because I am strongly opposed to belief in all forms of supernaturalism and paranormalism that have not been substantiated by the evidence. You know, ghosts, speaking to the dead, fairies, gods, poltergeists, psychic powers, astrology"