Your child sounds perfectly normal to me. DS is in the process of getting potty trained. They wear training pants and plastic pants over them at school -- even during nap time. Home it's hit or miss. He won't tell me he's gone potty in his pants, last Sunday he dropped a huge LOAD and he wasn't wearing a diaper. Not fun.
I recall last year one of the teachers who had a 3 year old at the daycare and complained that DD was trained at school (as were all her friends), but home -- no such deal.
Toddlers! Heck, DS has done this to us with other milestones -- walked for two months before we knew it, held his own bottle, fed himself. Must be a peer pressure issue