"A skeptic is one who prefers beliefs and conclusions that are reliable and valid to ones that are comforting or convenient, and therefore rigorously and openly applies the methods of science and reason to all empirical claims, especially their own. A skeptic provisionally proportions acceptance of any claim to valid logic and a fair and thorough assessment of available evidence, and studies the pitfalls of human reason and the mechanisms of deception so as to avoid being deceived by others or themselves. Skepticism values method over any particular conclusion." - Steven Novella
"What skeptical thinking boils down to is the means to construct, and to understand, a reasoned argument and, especially important, to recognize a fallacious or fraudulent argument. The question is not whether we like the conclusion that emerges out of a train of reasoning, but whether the conclusion follows from the premises or starting point and whether that premise is true." - Carl Sagan
I very much consider myself a skeptic. I think skepticism is much more important than atheism. I am an atheist because I am a skeptic. If the evidence pointed in favor of the existence of some sort of god, then I would stop being an atheist, but still be a skeptic. Also, the world is full of atheists who are not skeptics.
Too many people confuse skepticism with refusing to accept changes in conclusions regardless of what evidence is shown.
A good example of this are "climate change skeptics."
It doesn't matter how much evidence you show a climate change "skeptic," they will keep their same beliefs regardless.
Many Christians will claim to be similarly "skeptical" of atheism (e.g. "I don't have enough faith to be an atheist").
9/11 conspiracy nuts insist that they are "skeptical" of the "official version."
Anti vaccine nuts insist that they are "skeptical" of medical science.
Anti GMO nuts are also eager to tell you how "skeptical" they are of medical science.
People who believe in alternative medicine are also quick to mention how skeptical they are of evidence-based medical science (which in their jargon is "big pharma").
This of course denies what actual skepticism is. Actual skeptics are willing to change their conclusions when shown evidence that they are wrong, whereas most who describe themselves as skeptics are merely obstinate, delusional, and utterly impervious to arguments and evidence.