Others have responded abstractly with why this isn't a useful distinction, but I'll do you one better and give you a history lesson.

In 1649 Charles I of England was executed by order of Parliament. Parliament drew a distinction between the Crown and the person wearing it. Their loyalty was to the Crown. Having killed the King they decided to try being a republic.

Parliament is sovereign. But elected Heads of State are trouble - parliament eventually figured this out and got a new King instead.