International cricket
Most games are played as parts of "tours", when one nation travels to another for a number of weeks or months, and plays a number of matches of various sorts against the host nation. The ICC also organises competitions that are for several countries at once, including the Cricket World Cup & ICC T20 World Cup.
ICC Test Championship
The ICC Test Championship is an international competition run by the International Cricket Council for the 12 teams that play Test cricket. The competition is notional in the sense that it is simply a ranking scheme overlaid on all international matches that are otherwise played as part of regular Test cricket scheduling with no consideration of home or away status.