競 contest

立 (stand up) + 兄 (older brother)
★★★☆☆
20 strokes

Onyomi

KYOU

Mnemonic

KYOU (今日= today), My two older brothers stand up to have a contest with each other.

Kunyomi

きそ*う competing to get the best grade, the most sales. 90% overlapping with 競争; same useage and everything. fugeddaboutit.
★★☆☆☆

Jukugo

競争(きょうそう) する

competition ★★★☆☆
競 (contest) + 争 (battle) = 競争 (competition)

unless you're talking about a literal foot-race, 競争 does not mean a game. It refers to competing within a framework (usually business or academic). The best score on the test, the salesman who sold the most this month.

競走(きょうそう)

race ★☆☆☆☆
競 (contest) + 走 (run) = 競走 (race)

the more literal word for race: racing cars, sprinting, marathons, etc.

競馬(けいば)

horse racing ☆☆☆☆☆ FP
競 (contest) + 馬 (horse) = 競馬 (horse racing)

Synonyms

contest, game
試合    競争    競技    争う    勝負    競う    闘う