I would argue that few westerners actually believe there is little difference between the two.
The Japanese are one of the most distinct cultures in the world.
The West consumes tons of Japanese culture via anime, manga, video games, movies and music.
And every major Western city has a Chinatown where we get a glimpse of what China can be like.
Just by restaurants alone we can tell the major differences. Walk into a Japanese Ramen/Noodle house and it is tidy, clean, the staff welcomes you and they have unique accoutrements. Walk into a Chinese fast food restaurant and the walls have 10 years of grease on them, you can slide all over the greasy floors, the tables are rickety and sticky, there's a Chinese calendar on the wall and a lucky cat statuette near the cash register.
I think your stereotype of Westerners might be a little outdated by about 20 years.
