I'd say they are both relatively the same thing. Just different names.

I would start looking now on care.com

We will be looking for a full time nanny for June, July and August for an infant. We have daycare lined up starting in very late August. We are able to push back the start date until mid-June if that would get us a better nanny. I'm thinking this timeline makes it an attractive job for a student or a teacher.

When should I start looking?
Should I post on Care.com or Sittercity? Is one better than the other?