@Walter Hinteler,
That's the only difference, and it's meaningless. Governance proceeds from laws, not from the monarch. Law proceeds from the
res publica, the "public thing," not from the will of an individual. The last time any monarch attempted to impose his will was with William IV in 1831, when he refused a large creation of peers at the request of Earl Grey, and called on Wellington to form a government. Wellington was unable to do so, Lord Grey formed a government, and the Lords caved in rather than see such a creation of peers.
Functionally, Great Britain is a republic.