A basic assumption doing genealogy is that your family has a common root. There is an "Adam" from which the family grew. From this ancestor "Adam" the generations begin, and the family tree grows generation after generation. This implies that if you share a common surname, then you are descended from this "Adam". Readjusting ones thinking is necessary when dealing with Welsh surname such as JONES.
An act under Henry VIII entitled; "An act for laws and justice to be ministered in Wales in like form as it is in this realm." St. 27 Hen. VIII, c. 26 1535" (Stat. Realm, III. 563) states:
"...and that all and singular person and persons, born or to be born in the said principality country or dominion of Wales shall have enjoy and inherit all and singular freedoms liberties and rights privileges and laws within this his realm, and other the king's dominions, as other the king's subjects naturally born within the same have, enjoy and inherit."
It also goes own to state that the courts were to be held in English. Furthermore, it declares,
"...also that from henceforth no person or persons that use the Welsh speech or language shall have or enjoy any manner office or fees within this realm of England, Wales, or other the King's dominions upon pain of forfeiting the same offices or fees unless he or they use and exercise the English speech or language."
This in effect outlawed the Welsh language in the legal system of England. Thus it was during this period of history that the Welsh were required to use English surnames.
The table above gives an example of how a Welsh family might produce several different surnames, but share a common grandfather. For example, if Thomas was the grandfather [before the Act of Union], and had four sons, Richard, Edward, John, and David. When these four sons had their own family [after the Act of Union] , they would be required to used English in the realm's courts. Thus when their children , Peter, David, Thomas, and John had to use English, they would give their name Peter ap Richard, David ap Edward, Thomas ap John, and John ap David. The English clerks would then write down, Peter Richards, David Edwards, Thomas Jones, and John David. Four different surnames, but all "1st cousins".
After a generation or two, the surnames Richards, Edward, Jones and David would seem to be of different stock. But alas , they would be genetically related whereas others given the JONES surname would not! So, many of the Welsh surnames that were produced during this "Act of Union" produced a genetic bowel of spaghetti . Bon appetit!
The reference for the Act of Union is found in: "English Historical Documents, edited b C.H. Williams, Oxford University Press, NY, 1967.