"Zápasy" and "preteky", and something more about games, matches, races and competitions. I said back in January that games are all about chasing something (e.g. a
ball, as opposed to a wild animal like in hunting), while matches are about testing the equality of strengths or skills between two players or teams.
Race comes from an old German word for "current" (i.e. "prúd", of water rather than electricity), and competition comes from the Latin idea of "aiming or striving
together" towards a common objective, focusing nowadays on who can reach the objective first of all.
From this I'd say that "match" corresponds well with "zápas", especially in the original sense of wrestling, where two men test their relative strengths by trying to
grab each other "by the waist (or belt)" ("za pás"); and "race" corresponds with "preteky", where a group of people RUN (or drive, or ride) round a COURSE to test their relative speeds. But in
gymnastics, "competition" is a better translation of "preteky".