What's the difference between a sign written backwards and a sign written correctly?

There is no difference.

The formal writing of China ancient prose is to write a line vertically, then fill in a line from top to bottom, and then wrap the line from right to left. Therefore, ancient people in China studied from top to bottom and from right to left. For things that need to be written horizontally, such as banners on door couplets and plaques on doors, it is natural to write from right to left and read from right to left. After the Revolution of 1911, the Republic of China inherited this ancient writing method, so all the books and periodicals before the founding of the People's Republic of China were vertical editions, which should be read from top to bottom and from right to left.