Please explain briefly the hierarchy of Britain's nobility?

There is no real order as these are title given to someone. Even the royal line has the titles that you mentioned. For example along with with being Prince of Wales Charles also has the title Duke of Cornwall and Duke of Rothesay. His brother Prince Andrew is also know as the Duke of York (Andrew retains his title of prince making his daughters princesses by birth) Prince Andrew's ex wife Sarah Ferguson while married to Andrew was known as Princess Andrew, the Duchess of York. Only the wife of the heir apprant to the English court will be able to keep their first name like in the example Princess Diana's case.