The view of sex that most religions take is not that it's evil, but that it belongs within the confines of marriage. Thus, chastity is not a refusal to engage in sex, but a refusal to engage in sex outside marriage. A woman who practicies chastity has sex with her husband only; a woman who practices celibacy does not have sex. To be chaste is to bring the sexual urges under the dominion of your faith, not to merely deny them. People following an abstinence program (properly!) would be practicing chastity.
Sadly, there are far more public examples of people claiming to practice chastity who have failed, than of people who actually have held true to their principles; plus, proving that someone has done something is always easier than proving that someone HASN'T done something. Any person who abstains from sex before being married and avoids adultery while married would be said to practice chastity.