Do all innate immunity cells also serve in adaptive immunity

I know that B cells and T cells are unique to adaptive immunity. Are there cells unique to innate immunity?

Look here: http://en.wikipedia.org/wiki/White_blood…

All of the cells in the diagram are innate cells except for lymphocytes. Even then, NK cells are innate cells. Some of them become more activated by adaptive immune response, or act as antigen-presenting cells, but they are still solely innate immune cells.

Granulocytes, like neutrophils, eosinophils and basophils, are involved in innate immunity. Also, platelets perform an innate immune function, even though they aren't technically cells anymore.