Round trip - round trip

Japanese: 回回 - かいかい

...It was also used in Japan. In China, Islam began to be called Hui-Hui-Kyo (Korean 'Hui-Kyo') during the Ming Dynasty (1368-1643). The word originated from the word Hui-Hui, which was used to refer to the people of Central Asia during the Liao Dynasty (10th-11th century), and was a phonetic variation of the word Hui-Hui (Uighur), because there were many Muslims in Central Asia where the Hui-Hui lived.

From [Hui people]

...The population is about 8.6 million (1990). Historically, they are called Hui Hui or Hui people, but they call themselves Musilin (Muslims). The name Hui is a new one.

*Some of the terminology explanations that mention "kaikai" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…日本でも用いられた。中国でイスラムを回回教(回教)と呼ぶようになったのは明代(1368‐1643)である。その由来は，遼代(10～11世紀)に中央アジアの民族を呼ぶ回回という語があり，これは回紇(ウイグル)の語音の転じたもので，回紇が住んでいた中央アジアにイスラム教徒が多かったことによる。…