The two most obvious ones are the following:
1) Use of the third person limited (for Monsieur Loisel) versus the third person omniscient point of view(for Madame Loisel). The reader only gather information about the husband by what he says and does whereas for his wife, the reader "crawls inside her brain and heart" to know what she is thinking and feeling but not necessarily revealing to the other characters in the story. For example, Madame Loisel yearns for a luxurious apartment, dainty food, and beautiful clothes long before breaking down in front of her husband when they are invited to the gala. However, the reader knows this because her thoughts have been interwoven into the text.
2) Use of dialogue and body language indicators for character development, the latter being almost like stage directions written for a play. When Monsieur Loisel lifts the cover to the stew and relishes its aroma, the reader understands that he is a down-to-earth fellow who is satisfied with the simple pleasures of life (instead of brooding over the inattainable, as his wife does).
As Orwell's "Shooting an Elephant" is written in the first person point of view, I don't exactly see the parallel between this work and Maupassant's "The Necklace." "Shooting an Elephant" is a self-analytical study of why Orwell (actually, Eric Blair) had conformed so readily to others' expectations; it is written as a "mea culpa" (confession) of past mistakes. "The Necklace" is also a psychological study about self-esteem and conformity to others' expectations, only here the "confession" comes within the story line (and not directed to the reader) when Madame Loisel tells her old friend what exactly happened (she lost it) to the necklace she had borrowed ten years earlier.
The two stories then converge on theme, but (in my humble opinion) that is really about all they have in common.