Shiai (試合?) vs kyousou (競争?) in martial arts

Question

Within Shodokan Aikido, we practice something we call Randori (乱取り) in which two players fight one vs the other. Mostly, it is a tool for learning how to use Aikido versus a strongly resisting opponent. It is a learning tool and not used to determine who's best.

Shiai (試合?) is what we call the next level: it is a determination of who's best in that bout at this time. But there are no referees, no crowd, no medal, and no glory.

Kyousou (競争?) on the other hand is what we call shiai when there are referees, crowds, medals, and glory of winning a tournament.

Are we using all those terms correctly or have we made an utter mess of it?

Answer 1

The second one (it is a determination of who's best in that bout at this time. But there are no referees, no crowd, no medal, and no glory.) is called "練習試合{れんしゅうじあい}"

競争{きょうそう}(kyousou) means competition or bout in a very broad sense. There is not necessarily any implication of a sports match with a crowd, referees etc.

"宇宙{うちゅう}開発{かいはつ}競争{きょうそう}" "the space development race"

"乱取り" is a term meaning specifically the training of "合気道" or "柔道"

So you have three types of activities, "乱取り," "練習試合," and "（公式）試合."

"公式{こうしき}試合{しあい}" or "公式{こうしき}試合{じあい}"