In Othello, there are three women: Desdemona (upper class), Emilia (middle class), and Bianca (lower class). They also be categorized by their level of speech: Desdemona goes from being unquiet to quiet, while Emilia goes from being quiet to unquiet. (Bianca remains relatively quiet the entire play). Desdemona is a hero in Act I, but Emilia is the hero of Act V and overall.
As the daughter of a Senator, Desdemona enjoys great freedom of speech, especially in Act I. She advocates for herself in front of the Duke; she even openly rebels in front of her father. In Act I, Desdemona is a vixen, an unquiet, very modern woman.
But, after her marriage to Othello and move to Cyprus, Desdemona becomes an unquiet victim of male dominance. Desdemona seems like two different characters: why would the outspoken, rebellious Desdemona of Act I suddenly become silent, willingly letting Othello strangle her in Act V?
Emilia moves just the other way. Sure, Iago complains that she won't shut up, Emilia is rather quiet when we meet her in Act II. In her private conversations with Desdemona, however, we see that Emilia is the modern woman that Desdemona was in Act I. Emilia says that men exploit women: men are "stomachs, and we are but food." Finally, after Desdemona's murder, Emilia becomes the unquiet woman, openly disobeying her husband when his reputation and life are on the line: Iago says, "Get you home." Emilia replies, "I will not!"
After Iago stabs her, Emilia continues her unquietness:
O thou dull Moor! that handkerchief thou speak'st of
I found by fortune and did give my husband;
For often, with a solemn earnestness,
More than indeed belong'd to such a trifle,
He begg'd of me to steal it.
In fact, Emilia uses her dying words to not only expose her husband and Othello (and men in general), but she uses them to defend the murdered Desdemona. Contrast that with Othello's last monologue, in which he speaks only of his own reputation, and we see that Emilia is the true hero of the play.
In Othello, Desdemona and Emilia are similar in their honor to their husbands, yet they are strikingly different because their motivation comes from different areas. Both Desdemona and Emilia show honor and respect to their husbands Othello and Iago--the two women each respond to her husband's bidding. This is one of the factors that allows Iago to implement his scheme against Othello--Emilia takes the handkerchief without question. Yet the two women are in very different relationships, and this causes them to have different motivating factors. Desdemona and Othello have a relationship that is based on true love, and the two want to see each other happy. This motivates Desdemona to comply with Othello. But Emilia and Iago appear to have a relationship based on necessity--Iago does not speak kindly to Emilia nor does he show her any tenderness. Emilia is hardened, so she does not consider that her actions may have dire consequences when she takes the handkerchief. She is jealous of the relationship that Desdemona has, so in this case she does as Iago asks.