I use BGE a lot and when I play games, I find it's useful to be in texture view or material view versus solid view, because otherwise you can't see anything. What is the difference between these two settings? sometimes they seem different, but sometimes they look the exact same. In texture view, occasionally everything looks "shadeless" This happens when there are no lamps in the scene. But when there are lamps, both views are identical.
A fast approximation of the applied material. Some effects, such as procedural textures may not be shown.
Shows meshes with an image applied using the mesh’s active UV Map. The UV Map’s applied face texture will be shown.
Quoted from the manual.
The BGE does not support procedural textures, so in many cases Material and Textured view will look the same.
The difference comes when you have a texture on the object.
Material will only show the color for the object's material, never any textures.
Textured shows the active texture (even if you have turned off the texture in the texture tab of the properties window.)
(the Viewport Shading names make a lot of sense)