Different styles of Taekwondo prefer different Korean terms for sparring. Depending on the style, sparring can be called 겨루기 kyoroogi, 맞서기 matsogi, or 대련 daeryon.
If you train in Kukki-won Taekwondo (also called WTF Taekwondo or WT Taekwondo), then the preferred term for sparring is 겨루기 kyoroogi.
If you train in Changheon-yu Taekwondo (also called ITF Taekwondo), which is the style of Taekwondo promulgated by Choi Hong-hi, then the preferred term for sparring is 맞서기 matsogi. 맞서기 matsogi literally means ‘standing in opposition’ or ‘standing opposite each other’.
대련 daeryon is a term used by some Tangsudo schools. It was also used early on in Changheon-yu Taekwondo, and is occasionally still used today in some schools (though this is rare).
What should you not say?
Sparring in Taekwondo should not be referred to as kumite. This is a Japanese word that’s used to describe sparring in Karate. Korean is the proper language of Taekwondo, therefore Korean words should be used.
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Want to learn more?
If you'd like to learn more about the Korean terminology used in Taekwondo, consider buying this book: Taekwondo Terminology. It contains an extensive dictionary of terms used in Taekwondo, as well as explanations on how to pronounce Korean words, and aspects of Korean grammar.