Knockout (cup) and round robin (league) are the two classic tournament formats. In a knockout the winner goes through, and with seeding the strongest can only meet in the final; a number of entrants that isn't 2, 4, 8 or 16 gives byes. In a round robin everyone meets everyone once and the table decides the winner – it takes longer, but everyone gets more games.
Sources: Single-elimination tournament · Round-robin tournament