Say "into the final" for one deciding match (British usage: "the World Cup final") and "into the finals" for a final round or series of games ("the NBA Finals"). Informally, "the finals" is common for both.
One deciding match → 'the final'.
Final stage/series of games → 'the finals'.
BrE prefers 'final'; AmE often says 'finals' either way.
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Both exist — the right one depends on the competition.
The final (singular) = one deciding match. British English prefers it: "England got into the final of the World Cup."
The finals (plural) = a final round or series with several games: "the NBA Finals", "the finals of the tournament" (semi-finals + final together). Am