Thanks for your reply. My Davidsons were also associated with Richard Kennon in the 1700s (per at least one record that I found). I have not traced the Davies/Davis family. I guess it is always possible that some records that show that surname actually should have shown "Davidson" or "Davison," but this other family certainly did also exist.
David Davidson (sometimes shown as Davison) was married to a Sarah, and he left naturalization papers that state that he was born in Holland. A deed record shows that he owned land in James City Co., VA by at least 1682. His son, who was also named David Davidson, died in Charles City Co., VA in 1756, and a Stephen Davidson was the executor of his will (per a surviving court order book entry). I have never been able to determine who this son married.
It APPEARS that the children and/or grandchildren of the second David Davidson included the above Stephen Davidson, Hezekiah Davidson (my ggggg-grandfather), Ezekiel Davidson, Solomon Davidson, David Davidson, Edward Davidson, William Davidson and Philemon Davidson. There was also a William Davidson in James City Co., VA who also died there in 1687 (per a Bruton/Middleton Parish record). I do not know how/if he was related to the first David Davidson, and I do not know if some of the men mentioned above could have been out of this William Davidson versus out of the second David Davidson.