The Scarlet Letter

Where in the novel does it show the differences between female and male characters?

The scarlet letter itself is a depiction of the difference between male and female characters.  Hester Prynne is forced to wear the letter A upon her chest, as punishment for adultery, because she became pregnant prior to her husband's arrival in America. 

One major difference is how Hester is treated, because she is a woman and has obvious proof of adultery, and Arthur Dimmesdale, Hester's lover, who avoids public punishment because he remains unidentified.  He can hide his sin, she cannot.

"One of the most profound expressions of ambiguity surrounds Arthur, for it is the truth of sin that he keeps hidden which makes him the very pillar of moral purity in the community."

"In fact, exactly because he confesses his impurity he becomes a more powerful figure of virtue."

Hester spends her life on the edge of society, raising her daughter while dealing with the eternal damnation that the letter she wears suggests. 

"Society places her, identifying her as an adulteress and nothing more. She has no function in society except as an example for others’ behavior, regardless of her skills and caring nature, which become evident later in the novel."  

In the end Hester becomes stronger through her public punishment, while Arthur, who has hidden his sin, falters and dies under the protection that society has provided him all these years.