Sorry but why would anyone need to differentiate between a maid and a mother? I say hello and smile at anyone.
The only time maids annoy me is when they are the surly bored looking ones that don't look after the child properly..but this can be said for some mothers too!
Whether they are a maid or a mother is of no importance. How the child is looked after is the main thing.
I have to say, although not exactly this scenario, I was guilty of doing almost the same the other day. I was mortified when the second woman introduced herself. Glad it happened though. I looked like a t*at and learnt a lesson too. Sure she was aware of that. Too long in Dubai...