I guess I've always just heard "X Government Propaganda" as an idiomatic phrase used specifically to refer to things Government X tries to get its own citizens to believe on a long-term generational basis, turning it into "common wisdom." Whereas usually foreign-targeted propaganda is designed as part of a discrete operation to achieve some ephemeral goal, and it's the operation that has lasting relevance, not the propaganda itself (which is pretty quickly dispelled as soon as the next generation of foreigners grows up not having been touched by it.)

Or, to put it another way, domestic propaganda is strategic and continuous (and therefore easily observed, by meeting a citizen of the country who "grew up with the propaganda"); foreign-targeted propaganda is tactical and one-off, and won't usually leak out of whatever domain it was focused on (government, military, investors, entrepreneurs, etc.)