When we compare Madame Loisel's apparent situation and her true situation, we are looking at the difference between appearance and reality.
The difference between appearance and reality means that things are not what they seem. Madame Loisel is a very prideful woman. She is very vain about her appearance. This is the reason she borrows a necklace that she could never afford from her wealthier friend and makes her husband buy her a new dress so she can show off at the party.
The difference between appearance and reality is apparent at the party. We can see that Madame Loisel considers herself better than she is, because she focuses on her beauty.
The night of the ball arrived. Madame Loisel was a great success. She was prettier than any other woman present, elegant, graceful, smiling and wild with joy. All the men looked at her, asked her name, sought to be introduced. All the attaches of the Cabinet wished to waltz with her. She was remarked by the minister himself.
The author makes a point that Madame Loisel is “forgetting all” in this moment. She loves the attention, and therefore considers herself the equal of all of the upper class people at the ball. This forgetting is what leads to disaster. She is giving in to an illusion. She has one dress that she could not afford, bought with money her husband was saving up. She has the borrowed necklace. She has her beauty. She does not really belong there.
The necklace is another example of the illusion. When she loses it, she loses her beauty too. She has to work, and give up every last luxury she can afford, to pay back the loan for the necklace. Unfortunately, she finds out years later that the necklace too was an illusion.
"Yes. You never noticed it, then! They were very similar." …
Madame Forestier, deeply moved, took her hands.
"Oh, my poor Mathilde! Why, my necklace was paste! It was worth at most only five hundred francs!"
The necklace that she lost was not real, even though it looked real and expensive. However, she thought it was real and replaced it with a real one. She lost everything. She lost her beauty, and her relationship with her husband was strained in the process. Her pride got the best of her because she allowed herself to buy into an allusion that she could have a life that wasn’t hers.
The ball finally begins to break up at around four o'clock in the morning. Mathilde Loisel is one of the last to leave because she is having such a good time and is sought after by so many men. Then, like Cinderella, she is anxious to get away in a hurry. She does not want the other women to see that she does not have outer wrappings to go with her new gown and with the borrowed diamond necklace.
He threw over her shoulders the wraps he had brought, the modest wraps of common life, the poverty of which contrasted with the elegance of the ball dress. She felt this and wished to escape so as not to be remarked by the other women, who were enveloping themselves in costly furs.
These "modest wraps of common life" would betray the contrast between her apparent privileged situation in life and her true situation. It seems likely that the clasp of the necklace came undone when her husband "threw" the wraps over her shoulders and she was in such a great hurry to get away so that she would not be seen in such dowdy clothes by the other women, "who were enveloping themselves in costly furs." Maupassant says that her husband "threw over her shoulders the wraps he had brought." The word "threw" suggests, not that the husband was in any hurry to leave, but that he was in a bad mood after having had to wait so long while his wife was dancing and flirting with a lot of other men. Since the necklace was only a cheap imitation, it seems likely that the clasp was not a particularly good one and could have been easily knocked open. The necklace might not have fallen off immediately but might have dropped off anywhere during the Loisel's flight from the ball and their search for a cab.
Loisel held her back, saying: "Wait a bit. You will catch cold outside. I will call a cab."
But she did not listen to him and rapidly descended the stairs. When they reached the street they could not find a carriage and began to look for one, shouting after the cabmen passing at a distance.