From what I can find this depends on the definition, as there is a difference between a Signed Distance Function [0], and a Signed Distance Field, where the latter does get defined as a grid of values:
> A signed distance field is represented as a grid sampling of the closest distance to the surface of an object represented as a polygonal model. [1]
and
> Signed Distance Fields (SDF) are 3D textures where each texel stores the distance from the surface of an object. By convention, this distance is negative inside the object and positive outside. [2]
But that grid of values gets generated from either mathematical formulas, e.g. spheres, or from another representation of geometry such as a mesh or a vector shape.