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Below grade
Below grade means below the level of the surrounding ground, so a stump ground below grade sits under the soil surface instead of sticking up above it.
Grade is the level of the ground around a spot. Below grade means lower than that level. A stump ground below grade has its wood cut away beneath the soil surface.
The term matters when you plan what to do with the spot. If the stump is ground only to flush with the soil, the surface is level but little wood is removed underground. If it is ground below grade, there is a hole to fill, and the cut wood becomes stump grindings.
Illinois Extension says grinders can remove stumps to a depth ranging from flush to the soil line to over a foot deep. Purdue Extension says soil should be added to replace the below ground roots and stump. Ask what depth a quote includes. See after stump grinding.