A stair is made up of many parts and pieces. The two most common are the tread and riser. It sounds like you are referring to the riser which is the vertical element between the upper and lower tread.

In the case of a closed riser stair the riser is generally made up of a painted piece of wood. If your intent is to match the tread then the riser may very well be stained. Many people feel the species of wood they use on their stair should match their floors. This does provide a nice look but you can deviate if you want you stair to be a separate element. If this is the case you might want to consider hiring an architect or interior designer to help you select these materials.

Could you elaborate? I am not sure I understand you question. If you have a picture, I am sure that would be helpful as well.

I believe Dullea has it right! Risers can be painted to match other trim elements air built with the same species as the treads and stained and finished like the treads. It is a question of taste...and you end up deciding anyway! Look up stairs on Houzz and get feel for your favorite?