Morals are qualities that help us to do the right thing. A moral person would choose to do what is right, while an immoral person would choose to do what is best for him/her, even if it's the wrong thing to do. For example, if you have the opportunity to cheat on a test, would you? A person of good moral character would not. Morals are also the accepted beliefs of a society of what is right and wrong within society. Obvious morals of society are not stealing or killing. Moral character deals with a person who usually has an inner conflict. Do you help the kid who is being picked on by bullies, or do you just walk by and ignore it? Someone who is of good moral character does what's right, what's good, what is fair, and what's just, no matter what it costs that person.
In The Scarlet Letter, Dimmesdale doesn't do the right thing when he doesn't admit that he is Pearl's father. Sometimes a character in a novel changes and develops good moral character. Hester's husband changes for the worse. He becomes even more immoral as the plot develops.