When other “heads of state” visit the UK, they meet with the PM, in this case, May. They don’t meet with the queen in order to work out “heads of state” stuff.
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.