A VS Race in a mode featured in all Mario Kart games. This mode is pretty much similar to Grand Prix because you are racing on the same courses in Grand Prix. However, you do not win cups in a VS race. In Super Mario Kart (in this game, VS Race was called Match Race) to Mario Kart: Double Dash!! and Mario Kart 7, this mode was only playable through multiplayer. In Mario Kart DS and all games after that, this mode was in single player mode as well as multiplayer mode. This mode basically allowed you to race using the freedom to select the tracks you want to race on, and in Mario Kart DS and games after that, it featured more complex rules you can set, like the ability to race in teams, or set the difficulty of the CPU characters. This mode is basically used for multiplayer, or just for practicing racing on a course with other characters. In Mario Kart 7 and Mario Kart 8, it can also be played online.
In Mario Kart: Super Circuit, there's an unique gane mode known as Quick Run, which is similar to the single-player VS Races of later installments.