The US president is both head of state and government. That would make it a meeting between heads of government, in such cases where the POTUS meets with his equivalent head of government.
In other countries in Europe that do not have monarchs, the president is the head of state (but not head of government) and performs similar ceremonial duties to a monarch. That is usually the case with most parliamentary systems that are not constitutional monarchies.
Even in Canada, the prime minister is only head of government; the governor general acts as the head of state, being the Queen’s representative and viceroy, performing royal assent duties and also convening and dissolving the parliament, although the Queen is head of state.
The queen or monarch, or whatever you want to call her/them, are not legislators nor policy-makers, nor negotiators, nor head of the military or chief foreign policy decision-makers.
The monarchy, if it were to be dissolved, would not matter a bit when it comes to running the government. The queen and the entire monarchy are “disposable” and unneeded and just a remnant of their history, but with no “real power”. As such, the power belongs in parliament and in the prime minister.
So, what was the last real policy or decision made by the queen or the monarchy, which made a difference in how the UK runs the government and/or made a difference to anywhere else in the world, other than as the “unofficial head” of the country?