What is the relationship between Esther Summerson and Miss Barbary?

Esther thinks Ms. Barbary is her godmother, however, when she dies, Esther learns Miss Barbary was actually her aunt. Although she raises Esther with proper values, she lets her know that there is a dark secret surrounding her birth, and she never tells Esther anything about her birth mother or her circumstances. She is stern and judgmental, and Esther is a lonely child.