The Robin was voted as Britain's 'national' bird, whatever that may mean! It is not put off being close to humans and so has always been seen as a friendly bird. That, and the fact they have a nice red breast has seen them as a fixture on Christmas cards.
The American Robin is not related to the Robin found in the British Isles - they both feature some red that's about it!
I now see that Mary Poppins sang to an American Robin when she was supposed to be in London (but actually in Hollywood!)