In reply to my 3 October 2009 email to Louise Pettus as to whether Jane B. Springs was a d/o Richard Springs (1754 - 1833) and Jean Baxter (1761 - 1804), Louise replied:
I checked "The Squires of Springfield" by Katherine Wooten Springs (350 pages) and found no connection to the Fort Mill Springs family. But, as you no doubt know, there were more Springses in NC, especially in Mecklenburg.
In a follow-up email, Louise stated:
John Springs III was the son of Richard(1754 - 1833) who lived in Indian Land, northern part of Lancaster County. He (Richard) married Jean Baxter.