1. Korea drew the game against Japan.

2. Korea tied the game against Japan.

3. Korea and Japan drew in the game.

4. Korea and Japan tied in the game.

5. The game between Korea and Japan ended/finished in a draw.

6. The game between Korea and Japan ended/finished in a tie.
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Can we use both 'draw' and 'tie' in this way? Are they all grammatical?

To say "the game came to a draw" means that the teams tied. But to say a team drew ... means that the team will play the other team next or soon.

So here are the possibilities:

1. The game between Korea and Japan came to a draw.

2. Korea tied the game against Japan. OK

3. no

4. Korea and Japan were tied in the game.

5. The game between Korea and Japan ended/finished in a draw. OK

6. The game between Korea and Japan ended/finished in a tie. OK

Also ...

Korea drew Japan in the next round of games. (meaning that Korea and Japan will play in the next set of games)