So where is this different? And how? Who is funding this outside of the US and for what?

Apparently a lot of robotics work in Japan is aimed at assisting the elderly and making up for labor shortages.

Common topics here include assisting the elderly, industrial automation, disaster response, (minorly) entertainment, (minorly) consumer goods, and one other application area I studiously ignored because smart foreigners have no opinions about Article 9.

There were a couple of interesting discussions at the prefectural technology incubator about possible applications for research which was in the news at the time. It was a (very early prototype of a) man-portable cloaking device. Clearly, we decided, it was destined for the Tokyo fashion scene.

The japanese do a lot of robot research and AFAIK most of it is not military.

I'm not sure if the non-military clause in their constitution means they can't do military research.

The Japanese have a fairly large and technically advanced military, they just call it a "self-defense force". They can and do carry out military research.

Robotics research in Japan is primarily aimed at defending against giant space monster invasion. Oh wait, I guess that falls under defense.

you'd be all paranoid too if godzilla kept invading.

Ironically, it's the civilian sector that's limiting this research to the DoD. The FAA has very strict regulations on flying autonomous drones outdoors (basically, you're not allowed to do it), so this has seriously hobbled a lot of research into UAVs, etc. Israel, Canada, Western Europe and other places are far ahead now in terms of commercial autonomous drones.

In Japan, they'd like to use robots for earthquake rescue.

The US has similar research:

http://www.aaai.org/Pressroom/Releases/release-02-0910.php