SD mode is sort of RPG'ish with treasures you gain from winning battles and becoming a stronger fighter. it has the usual circuit, tournament and practice modes plus a 'treasure box' where you check your existing items, buy new items or trade items you already have for something else.
Virtual mode is the more familiar format of a battle game with game modes such as circuit, tournament and practice. It also has 2D and 3D "rules" for how the game is played. 2D is 16-bit arcade style and 3D is more realistic.