Reisen is a moon rabbit, and Watatsuki no Toyohime and Watatsuki no Yorihime's pet. She was one of the rabbits pounding medicine to atone for the crimes of Chang'e, but she hated her work so much that she fled to Earth. The tale of her escape is often written at the start of texts detailing the events of the Second Genso-Lunar War.
The Lunar Capital is a great city ruled by Lord Tsukuyomi that lies on the far side of the Moon. However, it's separated from the actual far side of the Moon by a protective barrier that makes it invisible from the outside. In this regard, it's similar to Gensokyo on Earth. Both Eirin Yagokoro and Kaguya Houraisan used to live in the Lunar Capital. As did Ringo and Seiran, but when they were dispatched to Gensokyo, they decided to remain there. There are many sages on the Moon, including Sagume Kishin, and the goddess Chang'e is also said to be imprisoned there somewhere. The Lunar Capital was once attacked by Junko, Hecatia, and Clownpiece.
The Capital is a city that only exists in certain universes. It's thought to have started out as the Lunar Capital, and the two have a lot in common. But there are a great many differences too.
Moon rabbits can communicate with one another telepathically, even if one is on the Moon and the other is on Earth. Such was the range of this ability. However, the rabbits of the Capital constructed the Moon Rabbit Network based on grid computing. No one rabbit plays a central role in the network. Instead, it collates each rabbit's excess thoughts to form a giant decentralized computing system. The system facilitates calculations and data analysis, chat boards and picture sharing, and the ever-suspicious dark web. However, it seems the majority of the functions are used in ways that serve no greater purpose at all.
Apparently, life in the Capital is a joyful thing.