This game is part of the beatmania IIDX series of music games that remained exclusively Japanese until 2006. beatmania IIDX 3rd Style: was the first of the PlayStation 2 games in the IIDX series. Previously, beatmania IIDX games were exclusively arcade games. This combines selected songs from styles 1, 2, and 3. Some songs were not included and remain arcade-exclusive.
beatmania IIDX 3rd Style removed the 4-keys mode from the game and replaced it with a Light7 difficulty. This gave most songs a completely separate, easier notechart. In addition, 3rd Style introduced Free Mode and Extra Stage.
Source: Wikipedia, "Beatmania IIDX 3rd Style", available under the CC-BY-SA License.