As far as i know it's the same Family, but i could be wrong. I live in Western, KY so records from Spartanburg are hard to come by.
Here is one hit that it is the same Family:
p. 127-128 Book F. April 29, 1797 David Allen (Spartanburg) to Young Allen (same) ; for 50 L sterling sold 150 ac ; border : Gocher's Cr, George Gibson, David Allen's Spring Br, and Jones; part of 543 ac grant Oct. 6, 1788 Gov. Thomas Pinckney to David Allen . Witness David Jones and Willis Allen. Signed David Allen's mark. Wit. Oath July 15, 1797 David Allen to John Lipscomb. Rec. Oct. 20, 1798
My ancestor is David's daughter Nancy Allen wife of Henry Gibson.