> I though there was a (blue?) one that japanese citizens could get, sent to their address.
No, there are no citizen specific IC cards unless you want extremely esoteric ones, like for senior citizens or children. All of the major nationwide mutual use transportation IC cards are freely available at the stations their operators carry. That's anything in the red box on this chart: https://en.wikipedia.org/wiki/Suica#/media/File:ICCard_Conne....
You can choose to register the card if you want to (add your name an other details). If you do this you can get your car back if lost. And, you can also get a commuter pass assigned (cheaper price between two stations for 1 month).
The red is a 30 day card for tourists. The green is valid for many years. You can get both anonymously, but there was a chip shortage a while back which meant only the red cards were widely available.
I though there was a (blue?) one that japanese citizens could get, sent to their address.