EHK raises good points.

I am currently doing research on the use of Cool Japan in Japanese national branding. The study is very much work in progress, so there are no definitive findings yet, but I can say a couple of things:

The shift from Japan Cool to Cool Japan does bear a significant shift in meaning. To my understanding, however, this shift has happened first outside of Japan rather than inside. Cool Japan -term is utilized in fan communities outside of Japan, and it is actively circulated by Japanese Studies, anthropology and media studies on Japan.

In Japanese politics Cool Japan was first officially used during Koizumi's last year in office. Taro Aso as minister of foreign affairs and PM made use of the term and took popular culture into his special attention.
Use of the term was also translated into policy decisions.
For instance MOFA made popular culture as part of embassies' official 'cultural diplomacy' abroad. It was during this time, that NHK's Cool Japan program was started (in 2006).

It appears that both terms Japan Cool and Cool Japan circulate both in and out of Japan and get different meanings depending on the context.
Nevertheless, the terms were taken into political use and national branding only after the phenomenon was recognized outside of Japan.
After that it has been used for both internal and external purposes.

Best,
Katja Valaskivi

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Dr. Katja Valaskivi (Ms.)
Assistant professor, docent
University of Tampere, Finland
School of Communication, Media and Theatre katja.valaskivi@uta.fi
+358-(0)50 396 9682