Swiss-style tournaments allow all participants to play in every round, pairing each player based on their current records. This ensures that players with similar records are paired together. Sometimes, it is not possible to pair players with exactly the same records, in which case you may be paired up or down. This means playing someone with a slightly worse or slightly better record.
In some Swiss tournaments, after the regular rounds (determined at the beginning of the tournament based on the number of players), the top X (usually 8) players go on to play a single-elimination playoff. When a player wins in the quarterfinals, they advance to the semi-finals, and so on.
In straight Swiss tournaments, once the Swiss rounds are over the tournament is complete and prizes are awarded based on the final standings. There is no top cut or playoff.