What can be seen above the ground is usually the tip of the iceberg when it comes to the size of the stump. Trees often flair at the bottom, and continue that flair below the surface. There are also roots that can be quite large running out from the stump, close to the surface.
Grinding the stump involves all portions of the stump at the soil line. Root chasing is following the large roots out from the tree stump and grinding them below the grade level.