The so-called six types of atheist, listed here alphabetically, are: activist (vocal about issues), anti-theist (assertive and outspoken), intellectual (philosophical and scientific), non-theist (apathetic), ritual (enjoy culture and ceremony), and seeker(open to different views).
Even the authors acknowledge that separating atheists in this way is arbitrary, and atheists can fall into more than one category. Many atheists prefer different labels, including agnostic, humanist, and freethinker. Depending on context, I put myself in these as well as all six of the atheist categories.
Most of my life I was a non-theist because I didn’t much care about my atheism. I became an activist atheist after moving to South Carolina and learning that the state’s Constitution prohibited atheists from holding public office. I worked for eight years to change that unconstitutional provision. As a curious intellectual who questions all religions, you could call me both a seeker and an anti-theist because I have the audacity to challenge religious belief. I also appreciate some religious ritual through godless Humanistic Judaism.
My biggest disappointment about the study is that it left out the largest category:closeted atheists. They are the elephants in the room and the ones most likely to change the culture by coming out. However, many of them feel they have good reasons not to, including potential ostracism from family and friends as well as loss of income or employment. Another unmentioned category is what I call functional atheists, those who may or may not have vague supernatural beliefs that play no practical role in their lives. They live as if there is no god, just as all atheists do.
An atheist is simply someone without a belief in any deities. But disbelief in gods doesn’t describe individual atheists any more than disbelief in the divinity of Muhammad, Krishna, and Zeus describes individual Christians. Everybody disbelieves in some gods; atheists just disbelieve in more gods than theists do.