This difference stems from traditional marriage customs. "Vdaná" basically means that the woman was "given" into the other family (traditionally she takes the husband's family name) so her family has taken care of that problem, "ženaty" means that the male in the family "got himself a wife (žena)", so for his family the problem of him running around has also been taken care of. Perhaps in the modern world "vdán" and "ženata" will also start making sense?
standelf and endless_sleeper already explained about the adjectives, but here's an explanation about the related verbs (source):
"At your wedding - svatba - marrying will be different if you are a man or a woman. For men, "to get married" is oženit se - literally " to take a wife" - and if you are a woman it is vdát se - literally "to give oneself." For those who prefer a third option, you can use the gender-neutral term vzít se - marrying each other."
So the man is beholden and the woman espoused? In English that just sounds ancient. Nowadays you say, "My sisters are married," and people are likely to answer with, "What, to each other?" It needs 'both' or 'all': like maybe "Moje sestry jsou obě vdané." or "Mé sestry jsou všechny vdané." (more likely "Všechny mé sestry jsou vdané.")