I insist that it's very possible to tell the difference between East Asians, for I have been several times to Korea and live in Japan. I flew quite a few times in planes composed half of Japanese and half of Korean and even flight attendant can usually tell the difference when they address someone (they have to know whether to speak in Korean or Japanese and rarely mistake). It is absolutely normal that Japanese can't tell the difference since most of them have never really thought about it or haven't been to Korea or China.
I did a little test, no later than last week in Incheon Airport (Seoul) trying to guess who was Japanese and who was Korean at the gate before boarding. I decided then approached to check what language they spoke. I got about 80% right. The hint is not in the clothes but in facial features, deeper and a bit more "Western" for Japanese, and rounder, flatter faces for Koreans. The eyes and smiles are a bit different too. You need to know a bit of both culture to recognise this. Koreans have squarer jaws too.
Some Chinese have darker or more "yellow" skin. They surely have squarer and harsher features than Japanese. This is certainly due to the life style and this difference is likely to disappear with time as Chinese will get richer and live more like Japanese. That is why, it's much more difficult to tell who's who if they live in the same country (Japan, US, etc). It's near impossible to tell a Korean or Chinese born and raised in Japan, because I believe the mentality (language) and lifestyle play the most important role in facial expression.