"We are going home."
Translation:Idziemy do domu.
Different cases and numbers. domu - genitive, singular; domy - nominative, plural; Different prepositions or different roles in sentence require different cases. In this case do requires genitive.
Here, you can find nearly full declension (lacs second option for vocative singular: domie)
I hear this every work day at about 3 seconds before I finish work from my polish friends :)
"Wracamy do domu." should also be accepted as it is we, and you are returning home. Therefore, the meaning is pretty much the same, and it should be accepted as both mean the same.