There are some similarities in both the melodic and harmonic structures of the tunes but there is one big difference: "She Goes Through the Fair" is in 4/4 time whereas "The Great Silkie of Sule Skerry" is in 3/4.
On a related note, my brain always confuses "Blackest Crow" and "Parting Glass" and they also differ in time signature. But the melodies are oh so similar.
Dusty T., Northern California
"A good song makes you laugh, it makes you cry, it makes you think."
-- Pete Seeger