not true, Wing can provide both lift and downforce, depending on its orientation.

Spoilers aren't supposed to provide downforce, AFAIK. If it distrubs airflow, it's called a spoiler, for obvious reason. If it provides downforce, it's called a wing.

 

Downforce is just upside down lift. Turn an airplane upside down and it'll be making downforce.

Spoilers ala NASCAR can create downforce. If they're done just right (shallow angle in the area of about 20 degrees) it can achieve the holy grail of aero, downforce and drag reduction, but both quantities will be relatvely small. Basically if it's steeply angled (maybe 60 degrees is the max you want to go for steepness) it makes downforce and drag, if it's closer to the horizontal it reduces drag and can create a little bit of downforce.