What is the basis of Gram staining results?

The structure of each cell type's wall.

Explanation:

The basis of Gram stain is differentiating cells in two different categories depending on the composition of the cell wall. Gram positives fixate a KI and Crystal Violeta complex in their peptidoglycan wall, but otherwise, gram negatives don't have a thick layer of this, and therefore, when the wash process happens it takes away all the pigments leaving the cells blank for the last pigment (pink).