Tartans aside: the Welsh certainly had a tribal/clan organization similar to the Highland Scots, but the history of how surnames were adopted is a bit different, and as a result most Welsh surnames are derived from Christian given names, which tells you little about a particular modern family's specific origin. In other words, if your name is Jones, and you're of Welsh descent (a pretty good bet if your name is Jones!), all you can tell is that your ancestor at the time surnames replaced patronymics was named John. Likewise if your name is Richards/Pritchard (ap Richard), or Reese/Rice/Price (ap Rhys), and so on. Clearly there would have been thousands of Welshmen named John, Richard, Thomas, and so on, most of them unrelated to and unaffiliated with each other, which is why the concept of a Clan Jones, Clan Rice, Clan Thomas, etc, doesn't really work in the Welsh context.

As a consequence, the Welsh heraldic system is very strange, seen from a Scottish or English perspective. Various major chieftains and princes who were living in the Middle Ages--a century or so before there was heraldry anywhere, and longer than that before it made its way to Wales--were subsequently and anachronistically "assigned" coats of arms, and people who are their descendants in the male line are entitled to bear those arms. And because the surnames weren't fixed until additional centuries after the arms were "assigned," these descendants might bear dozens of different surnames, even if they share a common male-line ancestor. Lay on top of that the granting and confirmation of other arms by the English heralds starting in the 16th century.

Bottom line: because of the way Lyon Office has operated for the last several centuries, fictively assuming that people with the same last name are related, even if we don't know how, you can often tell by the appearance of a Scottish coat of arms what the bearer's name is. That doesn't apply in England, and even less so in Wales.