The Welsh have been settling in the USA since colonial days and, as a result, there are millions of North Americans with Welsh last names. More and more Americans are finding a "Jones in their genes" as genealogy becomes increasingly popular in both countries.
In Wales, surnames were acquired in a very different way from that of England and Scotland. People in Wales were named and defined in relation to their father's Christian name. At first the naming system usually included "ab" or "ap" the Welsh word for "son", or "ferch" meaning daughter. As time went on, the "ap" part disappeared and Welsh began to adopt the fixed naming system of their English neighbors. However the B or P from "ab" or "ap" were often retained thus explaining why so many Welsh names begin with these two letters, for example, Bowen (from ab Owen) and Powell from (ap Howell).
Original Christian names often became surnames with an added s at the end. That is why we see so many examples of Williams, Morgans, Davies (after David) and Jones (after John).