Setting is important in both novels and short stories, but while novels will often have more than one setting a short story usually only has one. Thus, the short story is more highly dependent on the setting, and the setting is carefully chosen.
Short story settings are generally less complex than the settings of novels--of course because of the length of the work. Generally a novel will have multiple settings as well as more intricate development of mood and tone. It's kind of like the difference between a cheesecake bite and a whole piece of cheesecake--both are delightful.
Short story setting cover less of a range. Span of time, location, dates, seasons--all will be less because of the necessary nature of the shortened work. Novels will span a much larger range and variation.
Not only do locations vary in novels, but novels also often cover longer time spans than the short story, which, of course, is more confined in time as well as in space. Many novels, for instance, cover the life of a main character from youth to adulthood, whereas a short story is usually involved with one point in the character's life. Even if flashbacks are employed to allude to other parts, the main time period of the setting is still fixed.
The settings differ between short stories and novels in accord with the theories that govern their genres. Short stories focus on a single situation and a limited range of characters in what is called by the Encyclopedia Britannica an "economized setting." This means that there are restrictions to the scope of the setting, whereas in novels, there is no restriction to the scope of settings, either for description or location. For example, in the novel Pride and Prejudice, settings are sparingly described but locations abound. Elizabeth is at home, at Meryton, at Bingley's manor, at Rosings cottage, at Rosings manor, in Rosings park, in the lake district, at Pemberley.
Contrast this to a couple of short stories: "The Necklace": at home, at a ball, on a street, all in Paris; "A Rose for Emily": at Emily's home, in the streets of Emily's town; "Like White Elephants": at the train station. While short stories have range to the locations, they are nonetheless more restricted and focused than settings may be in novels. The reason for this is that short stories aim for a focused effect and part of the technique to gain this is by economizing the setting and refraining from fully developing them.
There is no real difference between a novel and a short story setting...some settings are more important than others. I have read short stories that have very detailed settings that are central to the plot, and I have read novels with no real description of the setting. It just depends on how important the setting is to the other elements in the text. Are you thinking of any texts in particular?
Novel is a type of story. The main distinguishing character of a novel that sets it apart from other forms of story is that it is a long story. Also novels are written in prose. There is no fixed standard for length of novels. But most novels exceed 60,000 words.
Two other basic features of a novel, including the two features mentioned above, together distinguish it from other kinds of literature. First, the story presented by a teller. This distinguishes it from a drama, which presents a story through the speech and actions of characters.
Second novels are works of fiction. In this they differ from histories, biographies, and other forms of prose literature that tell about real events, people or idea.
A story that is shorter than novel, which may be called a short story, is also a work of fiction like a novel. It usually centers upon a single incident or idea because of the length constraint.