Phi Delta Kappa and The National Sorority Phi Delta Kappa, Inc.
 

We only mentioned this once before on GC, and I am wondering if anyone out there could provide some insight.

There is a professional organization for educators called Phi Delta Kappa. There is also the National Sorority Phi Delta Kappa, Inc., which is a professional sorority made up of mostly black women teachers.

Is there any connection in their history at all?

Not that I can find. One is a professional organization founded at University of Indiana in 1906, the other a fraternity founded in New Jersey for Negro Women in 1923.