What is a difference between the British and Americans' thinking in The Canterville Ghost?
The British believe in tradition and aristocracy, whereas the Americans believe in pragmatic modernity and a republican (non-monarchial) form of government.
Ghosts haunting ancestral halls are part of the British tradition, so the English occupants of Canterville Hall have always accepted the reality of Sir Simon, the ghost, and have been suitably frightened by his appearances. The Otis family from America, on the other hand, initially refuses to believe in the ghost. When his presence becomes incontestable, they then refuse to be intimidated by him. Instead, they apply American know-how to the problems that he presents, washing away his bloodstains with Paragon Detergent and playing practical jokes on him. Sir Simon becomes more frightened of the Otis twins than the Otis family is of him.
At the end of the story, the American belief in the value of Republican simplicity comes to fore. Mr. Otis doesn't want his daughter to receive the ghost's gift of the Canterville jewels, as he thinks such costly items work against the American spirit. Mr. Otis says:
Under these circumstances, Lord Canterville, I feel sure that you will recognize how impossible it would be for me to allow them to remain in the possession of any member of my family; and, indeed, all such vain gauds and toys, however suitable or necessary to the dignity of the British aristocracy, would be completely out of place among those who have been brought up on the severe, and I believe immortal, principles of Republican simplicity.
Mr. Otis is also not initially impressed, as the British would be, that Virginia is marrying into the aristocracy by wedding a Duke. Mr. Otis's opinion is as follows:
Mr. Otis was extremely fond of the young Duke personally, but, theoretically, he objected to titles, and, to use his own words, "was not without apprehension lest, amid the enervating influences of a pleasure-loving aristocracy, the true principles of Republican simplicity should be forgotten."
However, Mr. Otis is proud when he walks Virginia up the aisle to be married, though we may imagine it is for other reasons than her marrying an aristocrat.
In the story "The Canterville Ghost," a main trait of the British is to believe in the historical superstitions of the house right away. The British owners know about the ghost and take it at face value. The house is haunted and nothing can be done. The British simply don't question the stories about the house and ghost.
On the other hand, the Americans do not believe in the ghost. They think that the British are simply being superstitious and archaic.
"But there is no such thing, sir, as a ghost, and I guess the laws of Nature are not going to be suspended for the British aristocracy."
Even as the Americans begin to believe that there might be something of merit to the ghost stories, they believe that superior modern day technology can rid the house of the ghost. That's why Washington Otis claims that his special stain remover can get rid of the stain. It's why Mr. Otis offers the ghost some special chain oil. The Americans view the ghost as something to be beaten and conquered, while the British view the ghost and something to tolerate and deal with.