Richard, I realize that I'm replying to a message that you posted more than five years ago, so I hope you're still following this forum.
The immigrant John Acheson had three sons, Matthew, Humphrey, and John. John Sr. sold a portion of his land in Little Britain, Lancaster Co., PA, to John Jr. in 1770. John Sr. died in 1778, and his widow sold the rest of the land to John Jr. in 1779. She then moved to Washington Co., PA, with sons Matthew and Humphrey.
I don't know anything more about John Jr., but if your Samuel is descended from this family, it is probably through him since he seems to have been the only one left in Lancaster County.