In Arthur Miller's "The Crucible", there are two characters that differ in every aspect: Abigail Williams and Elizabeth Proctor. This ranges from the way they handle situations, their personalities, to their social statuses, history and so forth.
Their social statuses can only be described as very contrasting: Abigail Williams is an orphan and the niece of Reverend Parris. She used to work as a servant for the Proctors, but her one night stand with John led to her dismissal by Elizabeth. Abigail is seen as very low, socially; as she is unmarried and an orphan (her parents were killed by American-Indians). The only people who are seen as lower than her are slaves (such as Tituba) and social outcasts.
On the contrary, Elizabeth is seen as a respectable woman as she is religious and married to a man of equal respect. We don't know much about her background, but she is highly regarded, has children with her husband and is a church-goer.
Personality-wise, Elizabeth and Abigail are incredibly different. Abigail is seen as sly but passionate and dominating. She is cunning and determined to get whatever she wants - everything that Elizabeth is not. Elizabeth is faithful, seen to be quiet and has definite religious beliefs. However from some aspects she is portrayed as cold and unforgiving, as she just can't seem to forgive John for being unfaithful, even seven months on from his confession. She strongly believes in religion and feels betrayed by her husband because of the one night stand and for breaking one of the Ten Commandments (adultery).
Lies play a massive role in "The Crucible" - another example of where Elizabeth and Abigail's characters clash. When Abigail receives power, she is happy to lie to get rid of Elizabeth and anyone else who got in her way or insulted her previously.