Is Edith Wharton’s realism similar to Henry James’s?

Yes, Edith Wharton's realism is similar to that of Henry James. Both came from wealthy American families and were friends and correspondents. Their similar backgrounds influenced their works.
Both novelists tried to use precise language (some complain that the late James was so precise as to be difficult to understand) to describe and analyze the psychological nuances of what life was like for individuals in upper-class circles. Both were also particularly interested in realistically describing the American upper-class experience. In this, both were different from rough-and-tumble authors of the American wilderness or western experience, such as James Fenimore Cooper or Mark Twain.
Instead, both Edith Wharton and Henry James concentrated on the drawing room and its refined manners. Novels such as James's The Portrait of a Lady and Wharton's The House of Mirth minutely explore the intersection of class, marriage, and wealth and the tragic effects the marriage market can have on beautiful young women. In both authors' work, it is the way people are seated or standing, the emphasis of a word, the import of a glance exchanged that make all the difference to a plot—psychological realism taken to a highly nuanced level.