The many countries in which the Head of State is distinct from the head of government include such widely diverse states as Israel, Germany, Italy and the Republic of Ireland.
And incidentally, when foreign Heads of State visit the UK, they do so as guests of the Queen, and their meetings with the head of government are incidental. When heads of government visit, the visit is downgraded to an Official Visit rather than a State Visit.
Among Western democracies/republics, the United States is rather unusual in having Head of State and Head of Government in the same person, though France is another example.
France’s Prime Minister, Édouard Philippe, is the head of government there, versus Macron who is head of state.