The meaning behind this would be that the differences are not of sort, type, or style, but of level, stage, or class.
Basically, 'degree' and 'kind' are generalizing words for different types of other words.
- Cats, dogs, and mice are kinds of animals.
- And first-, second-, and third-degree burns are degrees of burns.
DifferentiatingTo differentiate things by kind would mean to contrast or compare them.
Differentiating by degree would mean comparing things within a group of the same things, but on different stages/levels.