This article does not concern “modes” within gameplay, if say, you switch fighting styles and such (e.g. stances). Those vary very much in very specific ways between different games. This article concerns “modes” when selecting what to do when you boot up a game on a console, or occasionally when you begin arcade play.
There are certain modes you can select when you start a game on a port for home use. These typically include some, or perhaps all, of the following:
These are other modes, but they typically have little to do with actually playing the fighting games (e.g. involving mini-games, or a “store” where you may purchase extras).