Yeah tie can be both in sport.
It generally refers to a match, especially in a cup where the pairings are drawn. For example an “FA Cup tie”.
It can also mean where the scores end up the same. For example in cricket a tie is when both sides score the same number of runs with the last side batting having lost all their wickets. A draw is more usual. And in football when the match ends up with the same score, it’s called a draw, not a tie.