When Scout tells Miss Maudie that Atticus is the same inside his home as he is in public, she means that he doesn't handle disciplinary matters or personal matters any differently than he would "on the street." In fact, Scout specifically says that Atticus acts the same in the yard as he does in the house.
Men from this region (The South) and during this time frame, in particular, had a reputation of acting one way during church or in "polite society," but being someone totally different behind closed doors of their homes. For instance, while one might be mannerly and courteous out in company, that same man might be an abuser or a drunkard in the four walls of his house. Atticus, however, defies that stereotype: His behavior, attitudes, conduct, and refinement are the same no matter where he is. His regularity is a testament to his character, and he is respected as a result.
What they mean by stating that Atticus is the same in his house as he is in public is just that he does not put on a show in public to make others think he is better than he really is. Atticus does not change the way he acts or the way he treats people to earn their good opinion. He really is just a good person no matter who is around.
It is often easy to be on our best behavior in public, with our manners and courtesies in tact, but often when we enter our own homes, we treat our families in a much less kind manner than we do complete strangers. Atticus is not that way. He treats his children with as much respect as he does anyone in the community.
Atticus is different from others in town for just the reason described above. He is a good person through and through. He does not harbor resentments or revenge in his heart. He treats everyone with respect, regardless of wealth, race, or family. Most of the townspeople judge others based on their own ignorance, condemning them for the color of their skin or, in the case of Boo Radley, because they just don't understand them.
Good luck with your assignment! I hope this helps.
Atticus was a very dedicated father. This poured over into his work in the town. He was a man with very powerful ethics. He always allowed his children to experience life by things going on through town (The Tom Robinson Case). He never allowed them to judge others and Atticus always gave others a chance (Tom and Boo Radley).
Atticus was fair at his home as well as in public. He never had anything to hide and always conducted himself in an honorable manor.