In a group system — internationally called round robin — every team plays every other team in its group once. Nobody is eliminated: everyone plays all their matches and the final standings follow from the points.
In a knockout, half the field is out after every round. That is short and exciting, but whoever loses has played one match. In a group, how many matches everyone plays is fixed in advance — with four teams exactly 3, whatever the results.
Many tournaments combine the two: groups first so everyone plays enough, then a knockout between the best teams.
Every match yields points according to the chosen profile — in football 3 for a win and 1 for a draw. If two teams are level on points, a series of criteria decides in order: first the head-to-head result, then goal or set difference, then the head-to-head result between the remaining teams.
Because one big group produces a lot of matches. Twelve teams in one group is 66 matches; in three groups of four only 18. Several groups keep the tournament short and the wait between your own matches limited.
It is the English term for a system in which everyone plays everyone. A single round robin is once against each other, a double round robin is home and away — like a classic league season.
Technically as many as you like, but in practice four or five is the sweet spot. From six upwards the number of matches climbs quickly and the wait between your own matches gets long.
First it counts who won the match between them. If three teams are level, a mini-league between those three is created: only their matches against each other count. If they are still level, goal difference decides.