Generally speaking, no;however, there are a few weird exceptions to this rule: The same coat-of-arms CAN be granted in different countries. The same family sometimes has an alternative surname. In Polish heraldry, which operates along very different principles, not only can two individuals share a coat-of-arms, but entirely different FAMILIES can all share a coat-of-arms: the situation is entirely reversed from elsewhere in Europe, and, instead of a coat-of-arms belonging to a family, multiple families belong to a coat-of-arms. In the case you cite, was one family in Ireland and another in Scotland? Additionally, if a family has died out, its extinct arms could be re-granted to another family.