China. Neijia and Waijia. Nei=inside, wai=outside.
To add another data point or two to the discussion . . .
Something that I'd never picked up on until Mike Sigman brought it up years ago was the general connection, in the martial arts, between the internal/external classification and the Daoist/Buddhist classification, and the related sociopolitical impact of those terms. Simply put, the Big Three internal arts in China (taijiquan, xingyiquan, baguazhang) are basically Daoist in nature, while the external arts are generally derived from Shaolin gongfu, and therefore basically come from a Buddhist background. Given that basic distinction, one of the implications of the terminology is that -
Internal = Daoist = native Chinese, and
External = Buddhist = foreign in origin (Buddhism having come from India).
Add to that the fact that the Chinese word for China is "Central Kingdom", and foreigners are literally "outsiders" (waiguoren), and you can start to get a sense that there can be at least a subtly implied value judgement when using those terms in Chinese. Not all the time, but it does occur.
Having said all that, MIke is the only person I've read who talks about that definition of the term in relation to martial arts, but I think it is a useful aspect of the discussion to keep in mind, even if that aspect doesn't come into play as much in modern training.
Nei, "internal" is also used in the sense of "inner", with "inner" meaning "more important" or sometimes "secret", kind of like "inner circle" in English. One example would be the most important classic medical text in Chinese, the Huangdi Neijing - "The Yellow Emperor's Inner Classic", occasionally mistranslated as "The Yellow Emperor's Classic on Internal Medicine." The implication of the name is that because it is the "inner" classic, the really important information is in there, as opposed to the "outer" classic, the Huangdi Waijing (a text which is mentioned by name but which is probably lost).
My general impression following these discussions over the last few years is that "external" is now used more derogatorily than "wai" was probably used historically in China to describe these things. Although practicing "nei" arts is usually seen as being healthier for you and more conducive to longevity, which may come from the association with Daoism (which can be obsessed with longevity). Note that I'm talking about how people who practice "internal" arts talk about their own arts, not about the actual effect on longevity. I don't know if practicing internal arts actually is more or less healthy for you than gongfu or karate.