Match is one game e.g. Team A vs Team B at 5pm on Saturday. A competition is a organised event e.g. the Olympic games, or the World Cup. (Sorry I am not a volleyball expert, so I don't know the correct names of the competitions) There will be many different matches during a competition. For example, there are usually 4 quarter-final matches, 2 semi-final matches, and one final match. "Competition" also can be used more generally e.g. singing competition, hot dog eating competition. "Match" is generally only in sport.

Match is between two players or two teams (e.g. a football match, a tennis match). Competition is a more generic term, and can involve more than two subjects (e.g. competition among companies, a football world cup...)

A match is not a game in many sports. In volleyball, there are sets and matches, but colloquially people might use “game” for “set”. In tennis, a game is part of a set and a set is part of a match. Typically a competition will consist of a series of matches involving many competitors, with each match possibly comprising many games (“sets” in volleyball). In sports where each match is just one game (not volleyball), you can sometimes use both words (match, game) but it depends on the sport. For example, you wouldn’t usually talk about a “match” in American sports (baseball, basketball or American football), but you would for soccer. We would use “match” as a verb, but we would describe the events as “games” or “series” not “matches”. Or we would use “match up”. “This is a match up between two teams who need a win if they want to make a run for the playoffs.”