Asexuality describes an orientation, not a behavior, while celibacy is only talking about behavior. Someone who is celibate is not having sex by definition, while someone who is asexual doesnt experience sexual attraction, but they may or may not be having sex.

Is asexuality and celibacy the same thing?

Celibacy is a choice to abstain from sex, whereas for some asexuality is a lack of sexual attraction. Those who do not experience sexual attraction may choose to have sex for other reasons. Some asexual people may find sex off-putting, commonly referred to in the ace community as sex-repulsed.