A slab on grade is generally a concrete slab that bears directly on the ground and recives it support from the ground. A slab on grade is generally seperate from the foundation walls and does not carry any foundation loads (slab that is intregal with the walls and columns is a mat foundation). The basement floor especially in residential houses is usually a slab on grade. A slab that is supported by the walls and columns, such as the basement ceiling is refered to a suspended slab.
I qualify my answers somewhat because some people use these terms slightly differently, which yes can lead to some confusion. But if you were to say a slab on grade or suspended slab, this is what most people in the field would expect.