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I see a difference between a game and a match. At least in some sports they are not really interchangeable. But let's get more opinions.
In the US, "game" is probably used a lot more often than "match" because the most popular sports -- (American) football, baseball, basketball, and hockey -- are all referred to as "games." But other sports are played as a series of "games" (or sets) which together make up a "match."