A nanny, babysitter, and Au Pair all perform childcare activities to differing degrees.
A babysitter is hired to care for children casually and usually not on a daily basis.
A nanny is more involved with other household tasks and typically performs childcare, housekeeping, and other services for one family as a full-time job.
An Au Pair is a live-in nanny who is from a different country (or a different part of the country) who provides childcare that exposes children to new cultures or languages.