The Sigma Kappa and Gamma Phi Beta conundrum....
According to "From Here to Fraternity" by Robert Egan, this is what is says about Gamma Phi Beta:
"The Gamma Phi Betas were the first Greek letter-women's organization to call themselves a sorority, a word coined for them by a Syracuse Latin professor, six years after they were founded on that campus. Until that time, they had referred to themselves as a society. They have never called themselves a fraternity."

Sigma Kappa was founded November 9, 1874
Gamma Phi was founded November 11, 1874

Even though Sigma Kappa is older than Gamma Phi Beta by 2 days, I presume that GPHIB adopted the term "sorority" first. I do not know how Sigma Kappa referred to themselves in the early, early, days.

Sigma Kappa does have this "first" though, they are the first sorority founded in New England.