When creating a product group, you may see fields labeled "Distinguishing" and "Supplementary" attributes on the Update Product Group page. Distinguishing attributes are attributes that are specific to product (ie no two products would have the same distinguishing attributes). These are first seen on the Add Product page at the end of the Basic Information screen. 

Distinguishing attributes are used to create products in a product group and can be later edited in the Update Product Group screen in the Basic Information tab.

Supplementary attributes can be shared among any or all parts of a product group. 

For example, a product may have 4 variations of a shoe; 2 different sizes in 2 different colors. However, the material is the same for all 4 variations. The sizes and colors are Distinguishing attributes, but the material is a Supplementary attribute.

If a single product is being created as its own product group, the product will need at least one attribute associated with it. For example, a single scarf product have a size (One Size) and a color (Black). These attributes are helpful for someone using filtered navigation to look for a black scarf that is not size specific.